Question

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

Answer 1

Answer:

$x = \frac{ln(k)}{5}$

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

$x = \frac{ln(k)}{5}$