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{\frac{\ln(8) - 6}3}`