Question

log₄18 is-

• A. Rational
• B. Irrational
• C. Prime
• D. Composite

Answer 1

Answer: (B)

Irrational

Answer 2

log₄18 = $\frac{1}{2}$ [2 log₂3 + 1] = $\frac{p}{q}$ (p, q Î N)

log₂3 + $\frac{1}{2}$=$\frac{p}{q}$ ̃ log₂3 =$\frac{p}{q}$– $\frac{1}{2}$= $\frac{m}{n}$

Let m, n Î I and n ¹ 0

̃ 3 = 2^m/n

̃ 3ⁿ = 2^m

Which is not possible hence log₄18 is irrational.