Mathematics

Mathematics

Problem

(i) Express log⁡ax\log_{a}x in terms of the natural logarithm. (ii) Using the expression obtained in part (i), derive the formula for ddx(log⁡ax)\dfrac{d}{dx}\bigl(\log_{a}x\bigr). (iii) Evaluate ddx(log⁡5x)\dfrac{d}{dx}\bigl(\log_{5}x\bigr) at x=1x=1.

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