Question

If ${\log }_{a}3=2;{\log }_{b}8=3$, then ${\log }_{a}b=$

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

Answer 1

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

${\log }_{a}3=2\Rightarrow 3=a^2\Rightarrow a=3^{\frac{1}{2}}{\log }_{b}8=3\Rightarrow b=8^{\frac{1}{3}}=2$
$\therefore {\log }_{a}b={\log }_{\sqrt{3}}2={\log }_{3}4$