Question

Differentiate log₇ (2x − 3) ?

Answer 1

\[\text{ Let } y = \log_7 \left( 2x - 3 \right)\]

\[ \Rightarrow y = \frac{\log\left( 2x - 3 \right)}{\log7} \left[ \because \log_a b = \frac{\log b}{\log a} \right]\]

\[\text{ Differentiate it with respect to x we get }, \]

\[\frac{d y}{d x} = \frac{1}{\log7}\frac{d}{dx}\left\{ \log\left( 2x - 3 \right) \right\}\]

\[ = \frac{1}{\log7} \times \frac{1}{\left( 2x - 3 \right)}\frac{d}{dx}\left( 2x - 3 \right) \left[ \text{ using chain rule } \right]\]

\[ = \frac{2}{\left( 2x - 3 \right)\log7}\]

\[\text{ Hence }, \frac{d}{dx}\left\{ \log_7 \left( 2x - 3 \right) \right\} = \frac{2}{\left( 2x - 3 \right)\log7}\]