How do you differentiate #f(x) = log_x (3)#?

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Answer 1 · 2016-02-29T14:10:20

There are several ways to do this.

Method 1
Use change of base to write

#f(x) = ln3/lnx = ln3(lnx)^-1#

Now differentiate using the power and chain rules.

Method 2

#y = log_x3# #hArr# #x^y=3# #hArr# #ylnx=ln3#

Now differentiate implicitly.

Method 3

Use #f(x) = log_x3=1/log_3x = (log_3x)^-1#

Differentiate using the power and chain rules and derivative of logarithms with bases other than #e#.

#f'(x) = -1/(log_x3)^2*1/(xln3)#