Base Change Formula of Log
This formula is employed when expressing a logarithm of a number with a particular base as a ratio of two logarithms, each with a different base than the original logarithm. This is a logarithmic characteristic. The formula is given as:
logba = logca / logcb
or
logba . logcb = logca
Change of Base Formula
The change of base formula is a useful concept in mathematics. Especially when dealing with logarithms, It allows you to convert a logarithm from one base to another. Change of base formula in logarithm allows us to rewrite a logarithm with a different base. Instead of calculating the logarithm directly with the given base, we can use a different base and adjust the formula accordingly.
The significance of the change of Base Formula lies in its practical applications. It allows us to compute logarithms using calculators or computational tools that may only support logarithms with certain bases, typically base 10 (log10) or natural logarithms (ln). This formula is also useful in solving equations involving logarithms, simplifying expressions, and proving various mathematical identities.
Table of Content
- Change of Base Formula
- Base Change Formula of Log
- Derivation of Change of Base Formula
- Properties of Log Change of Base
- Solved Questions using Change of Base Formula