Question

Value of ${\log }_{4}18$ is:

• A. an irrational number
• B. a rational number
• C. natural number
• D. whole number

Answer 1

The correct option is A an irrational number

${\log }_{4}18={\log }_{2^2}\left({2.3}^2\right)=\frac{1}{2}{\log }_2\left({2.3}^2\right)$

$=\frac{1}{2}[{\log }_{2}2+{\log }_2{3}^2]=\frac{1}{2}[1+2.{\log }_{2}3]$

${\log }_{2}3$ is an irrational number.

Hence, $\frac{1}{2}[1+2.{\log }_{2}3]$ is also an irrational number.