Question

$lo{g}_{4}18$ 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

We know, $log\left(ab\right)=log\left(a\right)+log\left(b\right)$.
Also, $log\left(a^b\right)=b.log\left(a\right)$.
So, $lo{g}_{4}18=\frac{log2\times 3^2}{log4}=\frac{log2\times 3^2}{log{2}^2}=\frac{log2}{2log2}+\frac{2log3}{2log2}=\frac{1}{2}+\frac{log3}{log2}$.
As both $log2$ and $log3$ are irrational numbers, $lo{g}_{4}18$ is an irrational number too.