Find $x$ for $3^x = 5/3$ Why my answer is wrong? $3^x = 5/3$
$e^{\ln 3^x} = 5/3$
$e^{x \ln 3}=5/3$
$e^x \times e^{\ln 3} = 5/3$
$e^x \times 3 = 5/3$
$e^x = 5/9$
$x = \ln(5/9)$

$3^x=\frac{5}{3}\Leftrightarrow e^{x ln 3}=\frac{5}{3}$; as you see you have a mistake right after the first equal sign.
Try instead $$3^x=\frac{5}{3}|\log_3 \Leftrightarrow \log_3(3^x)=\log_3\left( \frac{5}{3}\right )$$
