Question

The value of
$\left(lo{g}_{3}2\right)\left(lo{g}_{4}3\right)\left(lo{g}_{5}4\right)\dots \left(lo{g}_{15}14\right)\left(lo{g}_{16}15\right)$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. 1

Answer 1

The correct option is C

$\frac{1}{4}$

The last 3 lines of the solution needs to change. It needs to made simple.

$\frac{log2}{log16}=\frac{log2}{log{2}^4}$

$=\frac{log2}{4log2}$ ...(Power law, $log{a}^m=mloga$ )

$=\frac{1}{4}$