Question

How do you solve `e^(3x)=5`?

Answer 1

Use properties of logarithms to find that `x = ln(5)/3`

Explanation:

We will be using the following properties of logarithms:

• `log(x^a) = alog(x)`

• `log_a(a) = 1`

Now, using the standard notation of the natural logarithm `ln(x)` to denote `log_e(x)` we have:

`e^(3x) = 5`

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

`=> 3xln(e) = ln(5)`

`=> 3x*1 = ln(5)`

`=>3x = ln(5)`

`:. x = ln(5)/3`