Question

If ${\log }_{a}3=2$ and ${\log }_{b}8=3$, then the value of ${\log }_{a}b$ is

• A. ${\log }_{3}2$
• B. ${\log }_{2}3$
• C. ${\log }_{3}4$
• D. ${\log }_{4}3$

Answer 1

The correct option is C ${\log }_{3}4$

$\frac{{\log }_{a}3}{{\log }_{b}8}=\frac{2}{3}$
$\Rightarrow \frac{{\log }_{a}b}{3{\log }_{b}8}{\log }_{2}3=\frac{2}{3}$
$\Rightarrow {\log }_{a}b={\log }_{3}4$
Ans: C