[tex]\bf log_2(x-2)-log_2(5)=1\\\\
-----------------------------\\\\
log_{{ a}}\left( \frac{x}{y}\right)\implies log_{{ a}}(x)-log_{{ a}}(y)\qquad thus\\\\
-----------------------------\\\\
log_2\left( \cfrac{x-2}{5} \right)=1\\\\
-----------------------------\\\\
{{ a}}^{log_{{ a}}x}=x\impliedby \textit{log cancellation rule}\\\\
-----------------------------\\\\
2^{\cfrac{}{}log_2\left( \frac{x-2}{5} \right)}=2^1\implies \cfrac{x-2}{5}=2^1
\\\\\\
\cfrac{x-2}{5}=2\implies x-2=10\implies x=12[/tex]
