Question

If e5x = k, where k is any positive number, then what is the value of X?

ap cal from edge. pls answer this question

Answer 1

`x = (ln(k))/(5)`

Step-by-step explanation:

Given

`e^(5x) = k`

Required

Solve for x

`e^(5x) = k`

Take natural logarithm of both sides:

`ln(e^(5x)) = ln(k)`

Apply law of logarithm:

`ln(e^(f(x))) = f(x)`

So, we have:

`ln(e^(5x)) = ln(k)`

`5x = ln(k)`

Divide through by 5

`x = (ln(k))/(5)`