How to solve for $x$ in $(16)^\frac{1}{x} = \frac{10}{3}$

Question

I don't know how to solve this equation: $$(16)^\frac{1}{x} = \frac{10}{3}$$

By the way this is coming from another equation so I've already solve half of it.

Answer 1

HINT:

$$16^{1/x}=\frac{10}3\implies \frac1x\log16=\log\frac{10}3\implies x=\cdots$$

Answer 2

$16^{1/x} = 10/3\implies {1\over x}\ln16=\ln 10 -\ln3 $. This follows from the rules for logarithms. Next,${1\over x}\ln16=\ln 10 -\ln3 \implies {1\over x} = {\ln 10-\ln3\over\ln16}$. Therefore, $x= {\ln 16\over\ln 10-\ln3}$. To clean this up, just use the rules for logs.