Question

score: 0 of 1 point
evaluate each of the following. give answers as integers or reduced fractions.
(a) \\(\ln\left(e^{3}\
ight) = \\) enter your answer
(b) \\(\ln\left(\frac{1}{e^{8}}\
ight) = \\) enter your answer

Explanation:

Step1: Use the logarithm property $\ln(a^b)=b\ln(a)$

For part (a), $\ln(e^{3}) = 3\ln(e)$. Since $\ln(e)=1$, then $3\ln(e)=3\times1 = 3$.

Step2: Rewrite the fraction and use logarithm properties

For part (b), $\ln(\frac{1}{e^{8}})=\ln(e^{-8})$. Using the property $\ln(a^b)=b\ln(a)$, we have $\ln(e^{-8})=-8\ln(e)$. Since $\ln(e) = 1$, then $-8\ln(e)=-8\times1=-8$.

Answer:

(a) $3$
(b) $-8$