Question

drag and drop the correct numbers into each box in the table below to indicate the value of each expression.

expression\tvalue
$log_{3}3^{3}$\t
$log_{10}(0.00001)$\t
$ln e^{-5}$\t

\t$-5$ $-3$ $-1$ $0$ $1$ $3$ $5$

Explanation:

Step1: Evaluate $\log_{3}3^{5}$

Using the logarithm power rule $\log_{a}a^{x}=x$, so $\log_{3}3^{5} = 5$.

Step2: Evaluate $\log_{10}(0.00001)$

Rewrite $0.00001$ as $10^{-5}$. Then $\log_{10}(10^{-5})=-5$ (by $\log_{a}a^{x}=x$).

Step3: Evaluate $\ln e^{-3}$

Using $\ln e^{x}=x$, so $\ln e^{-3}=-3$.

Answer:

For $\log_{3}3^{5}$: $5$
For $\log_{10}(0.00001)$: $-5$
For $\ln e^{-3}$: $-3$