JEE MainMathematicsEasyLogarithm and its applications

If $\log_{a}(ab) = x$ then $\log_{b}(ab)$ is equal to

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\log_{a}(ab) = x

\log_{a}a + \log_{a}b = x

\log_{a}b = x - 1

\log_{b}a = \frac{1}{x - 1}

\log_{b}a + \log_{b}b = \frac{1}{x - 1} + 1

\Rightarrow \log_{b}(ab) = \frac{1x}{x - 1}

Source: Grass-G / M-05 Mathematics Paper 10 October.docx

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