Question

log2(x-1)-log2(x+4)=-2

Answer 1

Careful

Answer 2

\[\log(a)-\log(b)\neq \log(ab)\]

Answer 3

Oh that was a minus sign... Silly me

Answer 4

\[\log_2(x-2)-\log_2(x+4)=\log_2\left(\frac{x-2}{x+4}\right)\]
So you get
\[\log_2\left(\frac{x-2}{x+4}\right)=-2\\
2^{(\cdots)}=2^{-2}\\
\frac{x-2}{x+4}=\frac{1}{4}\]