Question

Which expressions are equivalent to the one below? Check all that apply. ln(e^3)

Answer 1

Given:

$\ln(e^3)$

To find:

The equivalent expression.

Explanation:

Using the log rule,

$\ln a^b=b\cdot\ln a$

So, we write,

$\ln(e^3)=3\cdot\ln(e)$

We know that,

$\ln(e)=1$

Using this we get,

$\begin{gathered} \Rightarrow3(1) \\ \Rightarrow3 \end{gathered}$

Therefore, the equivalent expressions are,

$3\cdot\ln(e)\text{ and }3$

Final answer:

The correct options are A and D.