Question

What is the value of x if e^3x+6 = 8?

Answer 1

We can write any number n in the form $e^{\ln(n)}$, since $e^x$ and $\ln(x)$ are inverse functions, so that

$e^{3x+6} = 8 \iff e^{3x+6} = e^{\ln(8)}$

The bases are the same on both sides, so the exponents must be equal.

$3x + 6 = \ln(8)$

Solve for x :

$3x = \ln(8) - 6$

$x = \boxed{\dfrac{\ln(8) - 6}3}$