Differentiate the following functions with respect to `log x ​ 3`

Explanation

`text { Let } y=log _{x} 3`


`Rightarrow y=frac{log 3}{log x} quad[ log _{2} b=frac{log b}{log a}]`



Differentiate it with respect to `x` we get,


`Rightarrow frac{d y}{d x} =frac{d}{d x}(frac{log 3}{log x}) `


`=log 3 frac{d}{d x}(log x)^{-1}`


`=log 3 times[-1(log x)^{-2]} frac{d}{d x}(log x).`


`=-frac{log 3}{(log x)^{2}} times frac{1}{x} `


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