Question

If $\log_{4}5 = a$and $\log_{5}6 = b,$ then $\log_{3}2$is equal to

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

Answer 1

Answer: (D)

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

Answer 2

$ab = \log_{4}5.\log_{5}6 = \log_{4}6 = \frac{1}{2}\log_{2}6$

$ab = \frac{1}{2}(1 + \log_{2}3) \Rightarrow 2ab - 1 = \log_{2}3$

$\therefore$ $\log_{3}2 = \frac{1}{2ab - 1}$.