Question

Find the value of ${\log }_{8}512+{\log }_{2}8$

Answer 1

Let $a={\log }_{8}512+{\log }_{2}8$

$={\log }_8{8}^3+{\log }_2{2}^3$

$=3{\log }_{8}8+3{\log }_{2}2\dots (n{\log }_{a}b={\log }_a{b}^n)$

$a=3+3=6$

${\log }_{8}512+{\log }_{2}8=6$