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P3 - derivative of logx

Does anyone know how to solve this one:

Show that the derivative of log10x with respect to x is:
[pre] 1 [/pre]
xln10

Thanks for any help you can give.
Reply 1
Avatar for dvs
dvs
10
There are two ways you can do it:

1.
Using the "change of base" rule:
log10x = lnx/ln10
=> d[lnx/ln10]/dx = 1/(xln10)

2.
Let y = log10x.
10^y = x
e^[ln(10^y)] = x
e^[y ln10] = x

So:
dx/dy = ln10 e^[y ln10]
= ln10 . 10^y
= ln10 . x

Hence:
dy/dx = 1/(dx/dy)
= 1/(xln10)

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