Question

If $lo{g}_{4}5=a$ and $lo{g}_{5}6=b$, then, $lo{g}_3$ 2 is equal to

• A. $\frac{1}{2a+1}$
• B. $\frac{1}{2b+1}$
• C. $2ab+1$
• D. $\frac{1}{2ab-1}$

Answer 1

The correct option is D $\frac{1}{2ab-1}$

$\Rightarrow ab=lo{g}_{4}5.lo{g}_{5}6=lo{g}_{4}6=\frac{1}{2}lo{g}_{2}6$

$\Rightarrow ab=\frac{1}{2}(1+lo{g}_{2}3)\Rightarrow 2ab-1=lo{g}_{2}3$

$\therefore lo{g}_{3}2=\frac{1}{2ab-1}$