Question

Convert ln(3x) = 5 into exponential form. A) e3x = 5 B) e5 = 3x C) (ln)5 = 3x D) (3x)5 = ln

Answer 1

`\text{B)} \quad e^5=3x`

Explanation:

The exponential function and the natural log are inverse functions:

e^ln(x) = x

Using both sides of your given equation as exponents for e, we have ...

e^(ln(3x)) = e^5

From the above, we know that ...

e^(ln(3x)) = 3x

so we can substitute that into the preceding equation to get ...

3x = e^5

Swapping sides of the equal sign gives an equation that matches choice B:

e^5 = 3x