Question

Prove that:

${\log }_{2}10-{\log }_{8}125=1$

Answer 1

Now,

${\log }_{2}10-{\log }_{8}125$

$={\log }_{2}10-{\log }_{2^3}{5}^3$

$={\log }_2(5\times 2)-\frac{3}{3}{\log }_{2}5$ [ Using rule of logarithm]

$={\log }_2\left(2\right)+{\log }_{2}5-{\log }_{2}5$

$={\log }_{2}2$

$=1$.