Are your logs clear?

Let

$A : \log_{2} (x^{45}) = 45\log_{2} (x)$

$B : \log_{2} xy = \log_{2} x + \log_{2} y$

$C : \log_{3}x = \dfrac{1}{\log_{x}3}$

$D : \log_{3}8 = \dfrac{\log_{156}8}{\log_{156}3}$

$A$ is true.

$B$ is true iff $x>0$ .Thus correct statement should be $\log_{2} xy = \log_{2}\color{#3D99F6}{ |x|} + \log_{2}\color{#3D99F6}{| y|}$ .

$C$ is true only if $\color{#3D99F6}{x\neq1}$ .

$D$ is true. See here .