Differentiation of logs question (1 Viewer)

YashC3 · May 26, 2010

Differentiate:

3log2(x/5), where 2 is the base.

So basically differentiate 3log to the base of 2 (x/5)

Thanks

Drongoski · May 26, 2010

Can be done in many ways. One is:

$use:\ \ \ \frac{\mathrm{d} }{\mathrm{d} x}log_{a}x\ =\ \frac{1}{ln\ a}\cdot \frac{1}{x}\\ \\ if\ reqd\ can\ derive\ using\ change\ of\ base:\ \ log_{a}x\ =\ \frac{ln\ x}{ln\ a}\\ \\ so\ that:\ \ \frac{\mathrm{d} }{\mathrm{d} x}log_{a}x\ =\ \frac{1}{ln\ a}\frac{\mathrm{d} }{\mathrm{d} x}ln\ x\ =\ \frac{1}{ln\ a}\cdot \frac{1}{x}\ =\ \frac{1}{xln\ a}\\ \\ \\ \therefore \ \ \frac{\mathrm{d} }{\mathrm{d} x}3log_{2}\frac{x}{5 }\ =\ 3\ \cdot \frac{\mathrm{d} }{\mathrm{d} x} [log_{2}x\ -\ log_{2} 5]\ =\ 3\cdot [\frac{1}{xln\ 2}-\ 0]\ =\ \frac{3}{xln\ 2}$

YashC3 · May 26, 2010

cheers mate

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Differentiation of logs question (1 Viewer)

YashC3

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Drongoski

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YashC3

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