$10^{\log \left(x+3\right)} = 10^{2}$
$x + 3 = 100$
$x = 97$

$e^{\log (x+3)} = e^{2}$

$\ln\left(3x\right) = 4$
$e^{\ln \left(3x\right)} = e^{4}$

$\text{ln}\frac{x+4}{x}=2$

$e^{\text{ln}\frac{x+4}{x}}=e^{2}$

$\frac{x+4}{x}=e^{2}$

$x + 4 = xe^{2}$
$x − xe^{2} = −4$
$x\left(1 − e^{2}\right) = −4$

$x=\frac{-4}{1-e^{2}}\Rightarrow \frac{4}{e^{2}-1}$