how to solve for $x$ : $x\ln(4c)= \ln (c)$ where $c$ is a fixed parameter.

Question

How to solve $x \ln(4c)= \ln (c)$ for $x$? $c$ is a fixed parameter.

How do you multiple values in $\ln/\log$ and put it outside?

Answer 1

$$x\ln (4c)=\ln c \implies x=\frac{\ln c}{\ln (4c)}=\frac{\ln c}{\ln 4+ \ln c}, c>0, c \ne \frac{1}{4}.$$