If _4 5 = a and _5 6 = b, then _3 2 is equal to - Vidyadip

MCQ

If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to

A
${1 \over {2a + 1}}$
B
${1 \over {2b + 1}}$
C
$2ab + 1$
✓
${1 \over {2ab - 1}}$

✓

Answer

Correct option: D.

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

d
(d) $ab = {\log _4}5.{\log _5}6 = {\log _4}6 = {1 \over 2}{\log _2}6$

$ab = {1 \over 2}(1 + {\log _2}3) \Rightarrow 2ab - 1 = {\log _2}3$

$\therefore {\log _3}2 = {1 \over {2ab - 1}}$.

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