question what is the value of ln √5{e}? answer attempt 1 out of 3

Answer:

$\frac{1}{5}$

Explanation:

Step1: Rewrite the radical as an exponent

$\ln\sqrt[5]{e}=\ln e^{\frac{1}{5}}$

Step2: Use the logarithm - exponent property

Since $\ln a^b = b\ln a$, for $a = e$ and $b=\frac{1}{5}$, we have $\ln e^{\frac{1}{5}}=\frac{1}{5}\ln e$.

Step3: Evaluate $\ln e$

We know that $\ln e = 1$, so $\frac{1}{5}\ln e=\frac{1}{5}\times1=\frac{1}{5}$.