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$f(x) = 24 \cdot 4^x$ . Find $f(-1)$ .
Is $f(x) = 4 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 4 is greater than 1
3. A linear decrease
Is $f(x) = 10 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 10 is greater than 1
3. A linear decrease
Is $f(x) = 20 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 20 is greater than 1
3. A linear decrease
Is $f(x) = 22 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 22 is greater than 1
3. A linear decrease
Is $f(x) = 36 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 36 is greater than 1
3. A linear decrease
Is $f(x) = 12 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 12 is greater than 1
3. A linear decrease
Is $f(x) = 36 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 36 is greater than 1
3. A linear decrease
Is $f(x) = 25 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 25 is greater than 1
3. A linear decrease
Is $f(x) = 5 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 5 is greater than 1
3. A linear decrease
Is $f(x) = 10 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 10 is greater than 1
3. A linear decrease
Is $f(x) = 43 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 43 is greater than 1
3. A linear decrease
Is $f(x) = 17 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 17 is greater than 1
3. A linear decrease
Is $f(x) = 39 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 39 is greater than 1
3. A linear decrease
Is $f(x) = 36 \cdot \left(\tfrac{1}{ 2 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 2 }$
2. Growth, because 36 is greater than 1
3. A linear decrease
Is $f(x) = 16 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 16 is greater than 1
3. A linear decrease
Is $f(x) = 35 \cdot \left(\tfrac{1}{ 6 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 6 }$
2. Growth, because 35 is greater than 1
3. A linear decrease
Is $f(x) = 21 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 21 is greater than 1
3. A linear decrease
Is $f(x) = 50 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 50 is greater than 1
3. A linear decrease
Is $f(x) = 32 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 32 is greater than 1
3. A linear decrease
Is $f(x) = 19 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 19 is greater than 1
3. A linear decrease
Is $f(x) = 4 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 4 is greater than 1
3. A linear decrease
Is $f(x) = 37 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 37 is greater than 1
3. A linear decrease
Is $f(x) = 26 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 26 is greater than 1
3. A linear decrease
Is $f(x) = 14 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 14 is greater than 1
3. A linear decrease
Is $f(x) = 9 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 9 is greater than 1
3. A linear decrease
Is $f(x) = 3 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 3 is greater than 1
3. A linear decrease
Is $f(x) = 41 \cdot \left(\tfrac{1}{ 6 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 6 }$
2. Growth, because 41 is greater than 1
3. A linear decrease
Is $f(x) = 28 \cdot \left(\tfrac{1}{ 3 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 3 }$
2. Growth, because 28 is greater than 1
3. A linear decrease
Is $f(x) = 41 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 41 is greater than 1
3. A linear decrease
Is $f(x) = 13 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 13 is greater than 1
3. A linear decrease
Is $f(x) = 49 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 49 is greater than 1
3. A linear decrease
Is $f(x) = 7 \cdot \left(\tfrac{1}{ 6 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 6 }$
2. Growth, because 7 is greater than 1
3. A linear decrease
Is $f(x) = 49 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 49 is greater than 1
3. A linear decrease
Is $f(x) = 44 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 44 is greater than 1
3. A linear decrease
Is $f(x) = 29 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 29 is greater than 1
3. A linear decrease
Is $f(x) = 21 \cdot \left(\tfrac{1}{ 2 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 2 }$
2. Growth, because 21 is greater than 1
3. A linear decrease
Is $f(x) = 25 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 25 is greater than 1
3. A linear decrease
Is $f(x) = 21 \cdot \left(\tfrac{1}{ 6 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 6 }$
2. Growth, because 21 is greater than 1
3. A linear decrease
Is $f(x) = 46 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 46 is greater than 1
3. A linear decrease
Is $f(x) = 28 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 28 is greater than 1
3. A linear decrease
Is $f(x) = 47 \cdot \left(\tfrac{1}{ 5 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 5 }$
2. Growth, because 47 is greater than 1
3. A linear decrease
Is $f(x) = 15 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 15 is greater than 1
3. A linear decrease
Is $f(x) = 35 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 35 is greater than 1
3. A linear decrease
Is $f(x) = 11 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 11 is greater than 1
3. A linear decrease
Is $f(x) = 33 \cdot \left(\tfrac{1}{ 6 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 6 }$
2. Growth, because 33 is greater than 1
3. A linear decrease
Is $f(x) = 24 \cdot \left(\tfrac{1}{ 9 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 9 }$
2. Growth, because 24 is greater than 1
3. A linear decrease
Is $f(x) = 43 \cdot \left(\tfrac{1}{ 7 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 7 }$
2. Growth, because 43 is greater than 1
3. A linear decrease
Is $f(x) = 31 \cdot \left(\tfrac{1}{ 8 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 8 }$
2. Growth, because 31 is greater than 1
3. A linear decrease
Is $f(x) = 24 \cdot \left(\tfrac{1}{ 2 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 2 }$
2. Growth, because 24 is greater than 1
3. A linear decrease
Is $f(x) = 23 \cdot \left(\tfrac{1}{ 4 }\right)^x$ exponential growth or decay?
1. Decay: each step multiplies by $\tfrac{1}{ 4 }$
2. Growth, because 23 is greater than 1
3. A linear decrease
The graph of an exponential function passes through $(0, 8)$ and $(1, 16)$ . Write $f(x)$ .
Evaluate $\log_{ 4 } 16$ .
Solve $6^x = 21$ . Write the exact answer using a logarithm.
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 8 } y = 2$
2. $\log_{ 8 } y = 3$
3. $\log_{ 8 } y = -1$
4. $\log_{ 8 } y = \tfrac{1}{2}$
1. $y = 8^{2}$
2. $y = 8^{3}$
3. $y = \dfrac{1}{ 8 }$
4. $y = \sqrt{ 8 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 3 } y = 2$
2. $\log_{ 3 } y = 3$
3. $\log_{ 3 } y = -1$
4. $\log_{ 3 } y = \tfrac{1}{2}$
1. $y = 3^{2}$
2. $y = 3^{3}$
3. $y = \dfrac{1}{ 3 }$
4. $y = \sqrt{ 3 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 4 } y = 2$
2. $\log_{ 4 } y = 3$
3. $\log_{ 4 } y = -1$
4. $\log_{ 4 } y = \tfrac{1}{2}$
1. $y = 4^{2}$
2. $y = 4^{3}$
3. $y = \dfrac{1}{ 4 }$
4. $y = \sqrt{ 4 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 6 } y = 2$
2. $\log_{ 6 } y = 3$
3. $\log_{ 6 } y = -1$
4. $\log_{ 6 } y = \tfrac{1}{2}$
1. $y = 6^{2}$
2. $y = 6^{3}$
3. $y = \dfrac{1}{ 6 }$
4. $y = \sqrt{ 6 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 2 } y = 2$
2. $\log_{ 2 } y = 3$
3. $\log_{ 2 } y = -1$
4. $\log_{ 2 } y = \tfrac{1}{2}$
1. $y = 2^{2}$
2. $y = 2^{3}$
3. $y = \dfrac{1}{ 2 }$
4. $y = \sqrt{ 2 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 9 } y = 2$
2. $\log_{ 9 } y = 3$
3. $\log_{ 9 } y = -1$
4. $\log_{ 9 } y = \tfrac{1}{2}$
1. $y = 9^{2}$
2. $y = 9^{3}$
3. $y = \dfrac{1}{ 9 }$
4. $y = \sqrt{ 9 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 5 } y = 2$
2. $\log_{ 5 } y = 3$
3. $\log_{ 5 } y = -1$
4. $\log_{ 5 } y = \tfrac{1}{2}$
1. $y = 5^{2}$
2. $y = 5^{3}$
3. $y = \dfrac{1}{ 5 }$
4. $y = \sqrt{ 5 }$
Match each logarithm statement with the same statement written as a power.
1. $\log_{ 7 } y = 2$
2. $\log_{ 7 } y = 3$
3. $\log_{ 7 } y = -1$
4. $\log_{ 7 } y = \tfrac{1}{2}$
1. $y = 7^{2}$
2. $y = 7^{3}$
3. $y = \dfrac{1}{ 7 }$
4. $y = \sqrt{ 7 }$
An account holds 400 dollars and grows continuously at 3% per year. Write the amount $A(t)$ after $t$ years.
The area of mold is $f(t) = 2e^{ 4t }$ square millimetres after $t$ days. By what factor is the area multiplied each day? Give the exact value.
The graph of $y = \log_b x$ passes through the point $(9, 2)$ . What is $b$ ?
Where does the graph of $y = \ln(x - 3)$ cross the $x$ -axis? Give the value of $x$ .
What is the domain of $y = \ln(x - 6)$ ? Give it as an interval.
Here is the graph of $y = \log_{ 3 }(x - 5)$ . Tap the point where it crosses the $x$ -axis.
Evaluate $\log_{ 10 } 20 + \log_{ 10 } 5$ without a calculator.
Evaluate $2\log_{ 2 } 6 - \log_{ 2 } 9$ without a calculator.
Which expression is equal to $\log_{ 8 }(2 \cdot 7)$ ?
1. $\log_{ 8 } 2 + \log_{ 8 } 7$
2. $\log_{ 8 } 2 \cdot \log_{ 8 } 7$
3. $\log_{ 8 }(2 + 7)$
4. $7 \log_{ 8 } 2$
Which expression is equal to $\log_{ 7 }(4 \cdot 9)$ ?
1. $\log_{ 7 } 4 + \log_{ 7 } 9$
2. $\log_{ 7 } 4 \cdot \log_{ 7 } 9$
3. $\log_{ 7 }(4 + 9)$
4. $9 \log_{ 7 } 4$
Which expression is equal to $\log_{ 7 }(5 \cdot 3)$ ?
1. $\log_{ 7 } 5 + \log_{ 7 } 3$
2. $\log_{ 7 } 5 \cdot \log_{ 7 } 3$
3. $\log_{ 7 }(5 + 3)$
4. $3 \log_{ 7 } 5$
Which expression is equal to $\log_{ 7 }(5 \cdot 8)$ ?
1. $\log_{ 7 } 5 + \log_{ 7 } 8$
2. $\log_{ 7 } 5 \cdot \log_{ 7 } 8$
3. $\log_{ 7 }(5 + 8)$
4. $8 \log_{ 7 } 5$
Which expression is equal to $\log_{ 7 }(8 \cdot 9)$ ?
1. $\log_{ 7 } 8 + \log_{ 7 } 9$
2. $\log_{ 7 } 8 \cdot \log_{ 7 } 9$
3. $\log_{ 7 }(8 + 9)$
4. $9 \log_{ 7 } 8$
Which expression is equal to $\log_{ 8 }(3 \cdot 6)$ ?
1. $\log_{ 8 } 3 + \log_{ 8 } 6$
2. $\log_{ 8 } 3 \cdot \log_{ 8 } 6$
3. $\log_{ 8 }(3 + 6)$
4. $6 \log_{ 8 } 3$
Which expression is equal to $\log_{ 5 }(3 \cdot 4)$ ?
1. $\log_{ 5 } 3 + \log_{ 5 } 4$
2. $\log_{ 5 } 3 \cdot \log_{ 5 } 4$
3. $\log_{ 5 }(3 + 4)$
4. $4 \log_{ 5 } 3$
Which expression is equal to $\log_{ 5 }(2 \cdot 9)$ ?
1. $\log_{ 5 } 2 + \log_{ 5 } 9$
2. $\log_{ 5 } 2 \cdot \log_{ 5 } 9$
3. $\log_{ 5 }(2 + 9)$
4. $9 \log_{ 5 } 2$
Which expression is equal to $\log_{ 3 }(7 \cdot 4)$ ?
1. $\log_{ 3 } 7 + \log_{ 3 } 4$
2. $\log_{ 3 } 7 \cdot \log_{ 3 } 4$
3. $\log_{ 3 }(7 + 4)$
4. $4 \log_{ 3 } 7$
Which expression is equal to $\log_{ 6 }(7 \cdot 8)$ ?
1. $\log_{ 6 } 7 + \log_{ 6 } 8$
2. $\log_{ 6 } 7 \cdot \log_{ 6 } 8$
3. $\log_{ 6 }(7 + 8)$
4. $8 \log_{ 6 } 7$
Which expression is equal to $\log_{ 3 }(5 \cdot 6)$ ?
1. $\log_{ 3 } 5 + \log_{ 3 } 6$
2. $\log_{ 3 } 5 \cdot \log_{ 3 } 6$
3. $\log_{ 3 }(5 + 6)$
4. $6 \log_{ 3 } 5$
Which expression is equal to $\log_{ 9 }(7 \cdot 5)$ ?
1. $\log_{ 9 } 7 + \log_{ 9 } 5$
2. $\log_{ 9 } 7 \cdot \log_{ 9 } 5$
3. $\log_{ 9 }(7 + 5)$
4. $5 \log_{ 9 } 7$
Which expression is equal to $\log_{ 7 }(2 \cdot 5)$ ?
1. $\log_{ 7 } 2 + \log_{ 7 } 5$
2. $\log_{ 7 } 2 \cdot \log_{ 7 } 5$
3. $\log_{ 7 }(2 + 5)$
4. $5 \log_{ 7 } 2$
Which expression is equal to $\log_{ 6 }(2 \cdot 7)$ ?
1. $\log_{ 6 } 2 + \log_{ 6 } 7$
2. $\log_{ 6 } 2 \cdot \log_{ 6 } 7$
3. $\log_{ 6 }(2 + 7)$
4. $7 \log_{ 6 } 2$
Which expression is equal to $\log_{ 4 }(5 \cdot 9)$ ?
1. $\log_{ 4 } 5 + \log_{ 4 } 9$
2. $\log_{ 4 } 5 \cdot \log_{ 4 } 9$
3. $\log_{ 4 }(5 + 9)$
4. $9 \log_{ 4 } 5$
Which expression is equal to $\log_{ 3 }(5 \cdot 2)$ ?
1. $\log_{ 3 } 5 + \log_{ 3 } 2$
2. $\log_{ 3 } 5 \cdot \log_{ 3 } 2$
3. $\log_{ 3 }(5 + 2)$
4. $2 \log_{ 3 } 5$
Which expression is equal to $\log_{ 3 }(2 \cdot 6)$ ?
1. $\log_{ 3 } 2 + \log_{ 3 } 6$
2. $\log_{ 3 } 2 \cdot \log_{ 3 } 6$
3. $\log_{ 3 }(2 + 6)$
4. $6 \log_{ 3 } 2$
Which expression is equal to $\log_{ 4 }(9 \cdot 7)$ ?
1. $\log_{ 4 } 9 + \log_{ 4 } 7$
2. $\log_{ 4 } 9 \cdot \log_{ 4 } 7$
3. $\log_{ 4 }(9 + 7)$
4. $7 \log_{ 4 } 9$
Which expression is equal to $\log_{ 7 }(4 \cdot 3)$ ?
1. $\log_{ 7 } 4 + \log_{ 7 } 3$
2. $\log_{ 7 } 4 \cdot \log_{ 7 } 3$
3. $\log_{ 7 }(4 + 3)$
4. $3 \log_{ 7 } 4$
Which expression is equal to $\log_{ 8 }(5 \cdot 6)$ ?
1. $\log_{ 8 } 5 + \log_{ 8 } 6$
2. $\log_{ 8 } 5 \cdot \log_{ 8 } 6$
3. $\log_{ 8 }(5 + 6)$
4. $6 \log_{ 8 } 5$
Which expression is equal to $\log_{ 3 }(2 \cdot 7)$ ?
1. $\log_{ 3 } 2 + \log_{ 3 } 7$
2. $\log_{ 3 } 2 \cdot \log_{ 3 } 7$
3. $\log_{ 3 }(2 + 7)$
4. $7 \log_{ 3 } 2$
Which expression is equal to $\log_{ 2 }(5 \cdot 3)$ ?
1. $\log_{ 2 } 5 + \log_{ 2 } 3$
2. $\log_{ 2 } 5 \cdot \log_{ 2 } 3$
3. $\log_{ 2 }(5 + 3)$
4. $3 \log_{ 2 } 5$
Which expression is equal to $\log_{ 9 }(7 \cdot 8)$ ?
1. $\log_{ 9 } 7 + \log_{ 9 } 8$
2. $\log_{ 9 } 7 \cdot \log_{ 9 } 8$
3. $\log_{ 9 }(7 + 8)$
4. $8 \log_{ 9 } 7$
Which expression is equal to $\log_{ 7 }(4 \cdot 8)$ ?
1. $\log_{ 7 } 4 + \log_{ 7 } 8$
2. $\log_{ 7 } 4 \cdot \log_{ 7 } 8$
3. $\log_{ 7 }(4 + 8)$
4. $8 \log_{ 7 } 4$
Which expression is equal to $\log_{ 2 }(7 \cdot 6)$ ?
1. $\log_{ 2 } 7 + \log_{ 2 } 6$
2. $\log_{ 2 } 7 \cdot \log_{ 2 } 6$
3. $\log_{ 2 }(7 + 6)$
4. $6 \log_{ 2 } 7$
Which expression is equal to $\log_{ 8 }(2 \cdot 4)$ ?
1. $\log_{ 8 } 2 + \log_{ 8 } 4$
2. $\log_{ 8 } 2 \cdot \log_{ 8 } 4$
3. $\log_{ 8 }(2 + 4)$
4. $4 \log_{ 8 } 2$
Which expression is equal to $\log_{ 9 }(4 \cdot 7)$ ?
1. $\log_{ 9 } 4 + \log_{ 9 } 7$
2. $\log_{ 9 } 4 \cdot \log_{ 9 } 7$
3. $\log_{ 9 }(4 + 7)$
4. $7 \log_{ 9 } 4$
Which expression is equal to $\log_{ 7 }(6 \cdot 9)$ ?
1. $\log_{ 7 } 6 + \log_{ 7 } 9$
2. $\log_{ 7 } 6 \cdot \log_{ 7 } 9$
3. $\log_{ 7 }(6 + 9)$
4. $9 \log_{ 7 } 6$
Which expression is equal to $\log_{ 6 }(7 \cdot 9)$ ?
1. $\log_{ 6 } 7 + \log_{ 6 } 9$
2. $\log_{ 6 } 7 \cdot \log_{ 6 } 9$
3. $\log_{ 6 }(7 + 9)$
4. $9 \log_{ 6 } 7$
Which expression is equal to $\log_{ 9 }(6 \cdot 4)$ ?
1. $\log_{ 9 } 6 + \log_{ 9 } 4$
2. $\log_{ 9 } 6 \cdot \log_{ 9 } 4$
3. $\log_{ 9 }(6 + 4)$
4. $4 \log_{ 9 } 6$
Which expression is equal to $\log_{ 9 }(3 \cdot 2)$ ?
1. $\log_{ 9 } 3 + \log_{ 9 } 2$
2. $\log_{ 9 } 3 \cdot \log_{ 9 } 2$
3. $\log_{ 9 }(3 + 2)$
4. $2 \log_{ 9 } 3$
Which expression is equal to $\log_{ 3 }(8 \cdot 6)$ ?
1. $\log_{ 3 } 8 + \log_{ 3 } 6$
2. $\log_{ 3 } 8 \cdot \log_{ 3 } 6$
3. $\log_{ 3 }(8 + 6)$
4. $6 \log_{ 3 } 8$
Which expression is equal to $\log_{ 4 }(8 \cdot 5)$ ?
1. $\log_{ 4 } 8 + \log_{ 4 } 5$
2. $\log_{ 4 } 8 \cdot \log_{ 4 } 5$
3. $\log_{ 4 }(8 + 5)$
4. $5 \log_{ 4 } 8$
Which expression is equal to $\log_{ 2 }(4 \cdot 6)$ ?
1. $\log_{ 2 } 4 + \log_{ 2 } 6$
2. $\log_{ 2 } 4 \cdot \log_{ 2 } 6$
3. $\log_{ 2 }(4 + 6)$
4. $6 \log_{ 2 } 4$
Which expression is equal to $\log_{ 3 }(9 \cdot 5)$ ?
1. $\log_{ 3 } 9 + \log_{ 3 } 5$
2. $\log_{ 3 } 9 \cdot \log_{ 3 } 5$
3. $\log_{ 3 }(9 + 5)$
4. $5 \log_{ 3 } 9$
Which expression is equal to $\log_{ 3 }(8 \cdot 7)$ ?
1. $\log_{ 3 } 8 + \log_{ 3 } 7$
2. $\log_{ 3 } 8 \cdot \log_{ 3 } 7$
3. $\log_{ 3 }(8 + 7)$
4. $7 \log_{ 3 } 8$
Which expression is equal to $\log_{ 2 }(6 \cdot 9)$ ?
1. $\log_{ 2 } 6 + \log_{ 2 } 9$
2. $\log_{ 2 } 6 \cdot \log_{ 2 } 9$
3. $\log_{ 2 }(6 + 9)$
4. $9 \log_{ 2 } 6$
Which expression is equal to $\log_{ 3 }(7 \cdot 5)$ ?
1. $\log_{ 3 } 7 + \log_{ 3 } 5$
2. $\log_{ 3 } 7 \cdot \log_{ 3 } 5$
3. $\log_{ 3 }(7 + 5)$
4. $5 \log_{ 3 } 7$
Which expression is equal to $\log_{ 9 }(8 \cdot 7)$ ?
1. $\log_{ 9 } 8 + \log_{ 9 } 7$
2. $\log_{ 9 } 8 \cdot \log_{ 9 } 7$
3. $\log_{ 9 }(8 + 7)$
4. $7 \log_{ 9 } 8$
Which expression is equal to $\log_{ 8 }(6 \cdot 7)$ ?
1. $\log_{ 8 } 6 + \log_{ 8 } 7$
2. $\log_{ 8 } 6 \cdot \log_{ 8 } 7$
3. $\log_{ 8 }(6 + 7)$
4. $7 \log_{ 8 } 6$
Which expression is equal to $\log_{ 2 }(3 \cdot 5)$ ?
1. $\log_{ 2 } 3 + \log_{ 2 } 5$
2. $\log_{ 2 } 3 \cdot \log_{ 2 } 5$
3. $\log_{ 2 }(3 + 5)$
4. $5 \log_{ 2 } 3$
Which expression is equal to $\log_{ 6 }(3 \cdot 7)$ ?
1. $\log_{ 6 } 3 + \log_{ 6 } 7$
2. $\log_{ 6 } 3 \cdot \log_{ 6 } 7$
3. $\log_{ 6 }(3 + 7)$
4. $7 \log_{ 6 } 3$
Which expression is equal to $\log_{ 6 }(2 \cdot 5)$ ?
1. $\log_{ 6 } 2 + \log_{ 6 } 5$
2. $\log_{ 6 } 2 \cdot \log_{ 6 } 5$
3. $\log_{ 6 }(2 + 5)$
4. $5 \log_{ 6 } 2$
Which expression is equal to $\log_{ 9 }(8 \cdot 4)$ ?
1. $\log_{ 9 } 8 + \log_{ 9 } 4$
2. $\log_{ 9 } 8 \cdot \log_{ 9 } 4$
3. $\log_{ 9 }(8 + 4)$
4. $4 \log_{ 9 } 8$
Which expression is equal to $\log_{ 3 }(2 \cdot 8)$ ?
1. $\log_{ 3 } 2 + \log_{ 3 } 8$
2. $\log_{ 3 } 2 \cdot \log_{ 3 } 8$
3. $\log_{ 3 }(2 + 8)$
4. $8 \log_{ 3 } 2$
Which expression is equal to $\log_{ 7 }(3 \cdot 9)$ ?
1. $\log_{ 7 } 3 + \log_{ 7 } 9$
2. $\log_{ 7 } 3 \cdot \log_{ 7 } 9$
3. $\log_{ 7 }(3 + 9)$
4. $9 \log_{ 7 } 3$
Which expression is equal to $\log_{ 7 }(3 \cdot 2)$ ?
1. $\log_{ 7 } 3 + \log_{ 7 } 2$
2. $\log_{ 7 } 3 \cdot \log_{ 7 } 2$
3. $\log_{ 7 }(3 + 2)$
4. $2 \log_{ 7 } 3$
Which expression is equal to $\log_{ 8 }(9 \cdot 2)$ ?
1. $\log_{ 8 } 9 + \log_{ 8 } 2$
2. $\log_{ 8 } 9 \cdot \log_{ 8 } 2$
3. $\log_{ 8 }(9 + 2)$
4. $2 \log_{ 8 } 9$
Which expression is equal to $\log_{ 5 }(3 \cdot 7)$ ?
1. $\log_{ 5 } 3 + \log_{ 5 } 7$
2. $\log_{ 5 } 3 \cdot \log_{ 5 } 7$
3. $\log_{ 5 }(3 + 7)$
4. $7 \log_{ 5 } 3$
Which expression is equal to $\log_{ 4 }(2 \cdot 8)$ ?
1. $\log_{ 4 } 2 + \log_{ 4 } 8$
2. $\log_{ 4 } 2 \cdot \log_{ 4 } 8$
3. $\log_{ 4 }(2 + 8)$
4. $8 \log_{ 4 } 2$
Write $\log_{ 3 } x + 2\log_{ 3 } 4$ as a single logarithm.
Expand $\log_{ 8 }\left(\dfrac{x^{ 4 }}{y^{ 5 }}\right)$ : write it with logarithms of $x$ and $y$ only.
Solve $6^x = 35$ . Give the exact answer using natural logarithms.
Solve $2\cdot 3^x = 48$ . Give the exact answer.
A sample of 64 mg of a radioactive substance has a half-life of 2 years. How many mg are left after 6 years?
A dose of 200 mg of a medicine has a half-life of 2 hours. Write the amount $A(t)$ , in mg, left after $t$ hours.
A sample of 200 mg has a half-life of 2 years. How much is left after 8 years? Round to 2 decimal places.

Answers

$6$
Decay: each step multiplies by $\tfrac{1}{ 4 }$
$8 \cdot 2^{x}$
$2$
$\frac{\ln{\left(21 \right)}}{\ln{\left(6 \right)}}$
$\log_{ 8 } y = 2$ → $y = 8^{2}$ · $\log_{ 8 } y = 3$ → $y = 8^{3}$ · $\log_{ 8 } y = -1$ → $y = \dfrac{1}{ 8 }$ · $\log_{ 8 } y = \tfrac{1}{2}$ → $y = \sqrt{ 8 }$
$400 e^{\frac{3 t}{100}}$
$e^{4}$
$3$
$4$
$(6, \infty)$
$(6, 0)$
$2$
$2$
$\log_{ 8 } 2 + \log_{ 8 } 7$
$\frac{\ln{\left(16 x \right)}}{\ln{\left(3 \right)}}$
$\frac{4 \ln{\left(x \right)}}{\ln{\left(8 \right)}} - \frac{5 \ln{\left(y \right)}}{\ln{\left(8 \right)}}$
$\frac{\ln{\left(35 \right)}}{\ln{\left(6 \right)}}$
$\frac{\ln{\left(24 \right)}}{\ln{\left(3 \right)}}$
$8$
$200 \cdot 2^{- \frac{t}{2}}$
$\frac{25}{2}$ mg