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.

Step-by-step 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.