We can write any number n in the form [tex]e^{\ln(n)}[/tex], since [tex]e^x[/tex] and [tex]\ln(x)[/tex] are inverse functions, so that
[tex]e^{3x+6} = 8 \iff e^{3x+6} = e^{\ln(8)}[/tex]
The bases are the same on both sides, so the exponents must be equal.
[tex]3x + 6 = \ln(8)[/tex]
Solve for x :
[tex]3x = \ln(8) - 6[/tex]
[tex]x = \boxed{\dfrac{\ln(8) - 6}3}[/tex]
