Question

Simplify
${log}_{27}9+{log}_{8}4$

Answer 1

$lo{g}_{27}9+lo{g}_{8}4$

$\Rightarrow lo{g}_3^{3}9+lo{g}_2^{3}4$

$\Rightarrow \frac{1}{3}lo{g}_{3}9+\frac{1}{3}lo{g}_{2}4$

$\Rightarrow \frac{1}{3}lo{g}_3{3}^2+\frac{1}{3}lo{g}_2{2}^2$

$\Rightarrow \frac{2}{3}lo{g}_3^3+\frac{2}{3}lo{g}_2^2$

$\Rightarrow \frac{2}{3}+\frac{2}{3}=\frac{4}{3}$.