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$\log_{4} 29$

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

Which of the following are correct about physisorption?

1) Decrease in entropy of system
2) Decrease in enthalpy
3) The value of TdS is positive
4) It is reversible in nature