Simplify without using tables log26log28 l o g 2 6 l o g 2 8 - log23log212

Simplify without using tables $\frac{lo{g}_{2}6}{lo{g}_{2}8}$ - $\frac{lo{g}_{2}3}{lo{g}_2\frac{1}{2}}$

Answer Details

log26 - log23 = log2 ($\frac{6}{3}$) = log22
log28 - 2$\frac{1}{2}$ log28 - log2$\frac{1}{2}$ log28 - log2$\frac{1}{4}$
$\frac{lo{g}_{2}2}{lo{g}_{2}32}=\frac{lo{g}_{2}2}{5lo{g}_{2}2}$
= $\frac{1}{5}$
N.B. log22 = 1