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

We know that $a^x = e^{x \ln a}$
thus $3^x = e^{x \ln 3} = 5/3$
applying $\ln$ to both sides, we get $x \ln 3 = \ln (5/3) = \ln(5) - \ln(3)$
The rest is straightforward algebra:
$$x \ln 3 + \ln 3 - \ln 5 = 0$$
$$(x+1) \ln 3  = \ln 5$$
$$x + 1 = \ln 5 / \ln 3$$
$$x = \frac{\ln 5}{\ln 3} - 1$$
