solve for x

$\displaystyle 3^{x} e^{7x+2} = 15 $

$\displaystyle 3^{x} e^{7x} e^{2} = 15 $

$\displaystyle 3^{x} e^{7x} = \frac{15}{e^{2}} $

$\displaystyle ln (3^{x} e^{7x}) = ln\frac{15}{e^{2}} $

$\displaystyle ln 3^{x} + lne^{7x} = ln\frac{15}{e^{2}} $

$\displaystyle x(ln3 +7) = ln \frac{15}{e^{2}} $

$\displaystyle x = \frac{ln \frac{15}{e^{2}}}{ln3 +7} $

is this correct?