Factoring ln functions

Question

can anyone tell me how the following factoring ends in $\ln x - \frac{ln 2}{2}$

Original

$\frac{\ln x}{\ln 2} - \frac{\ln 2}{ln 2}$

Work shown from Professor

$\frac{1}{ln 2} (\ln x - \frac{ln 2}{2})$

Answer 1

It's not. Clearly, the original evaluated at $x=0$ is $-1$ while your professor's factored form evaluated at $x=0$ is $-\frac{1}{2}$