Change of Base Formula

The Change of base formula helps to rewrite the logarithm in terms of another base log. Change of base formula is used in the evaluation of log and have another base than 10.

\[\LARGE \log_{b}x=\frac{\log _{d}x}{\log _{d}b}\]

Solved Examples

Question 1: Solve 2$\log_{4} 29$
Solution:

Given 2$\log_{4} 29$
Using logarithm change of base formula,

$log_{b} x$ = $\frac{log_{d} x}{log_{d} b}$

2$\log_{4} 29$ = 2$\times$ $\frac{log_{10} 29}{log_{10} 4}$

2$\log_{4} 29$ = 2 x 2.43 = 4.86

Practise This Question

A random variable X has the following probability distribution
XP(X=x)XP(X=x)0λ511λ13λ613λ25λ715λ37λ817λ49λ
then, λ is equal to