Question

The value of ${\log }_{4}18$ is equal to

• A. a rational number
• B. an irrational number
• C. a prime number
• D. none of these

Answer 1

Answer: (B)

an irrational number

$lo{g}_{4}18$

$=\frac{log18}{log4}$

$=\frac{log2+log9}{2log2}$

$=\frac{log2+2log3}{2log2}$

$=\frac{log2}{2log2}+\frac{2log3}{2log2}$

$=\frac{1}{2}+lo{g}_{2}3$

Since $lo{g}_{2}3$ is irrational.

Hence

$\frac{1}{2}+lo{g}_{2}3$ is irrational.

Therefore

$lo{g}_{4}18$ is an irrational number.