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 $\frac{1}{2ab-1}$

$ab=lo{g}_{4}5.lo{g}_{5}6=lo{g}_{4}6=\frac{1}{2}lo{g}_{2}6$
$ab=\frac{1}{2}(1+lo{g}_{2}3)\Rightarrow 2ab-1=lo{g}_{2}3$
$\therefore lo{g}_{3}2=\frac{1}{2ab-1}$