The value of $ \frac{\log_{a}{x}}{\log_{ab}{x}}

The value of $ \frac{\log_{a}{x}}{\log_{ab}{x}} - \log_{a}{b}$ is ?

1. 0
2. 1
3. a
4. ab

Correct Option: B

∵ log_a x = ( log_abx) / (log_aba)
∴ The given expression = [[(log_abx) / (log_aba)] / [( log_abx )] - ( log_ab)
= (1/log_aba) - log_ab = log_aab - log_ab = log_a(ab/b)
= log_aa = 1

Logarithm

Aptitude

Correct Option: B