Question

Which expressions are equivalent to the one below? check all that apply

ln(e^3)
A. 1
B. 3
C. 3*ln e
D. 3e

Answer 1

Option B and C.

Explanation:

The given expression is

`\ln (e^3)`

Using the power property of exponents we get

`3\ln (e)`
`\because \ln a^n=n\ln a`

We know that ln is the natural log, it ln means log with base e. So ln(e)=1.

Substitute ln(e)=1 in the above equation.

`3(1)`

`3`

The expressions 3ln(e) and 3 are equivalent to the given expression.

Therefore, the correct options are B and C.