How do you differentiate #y= log _3 x#?

1 Answer
Nov 4, 2016

#(dy)/(dx)=1/(xln3)#

Explanation:

We can't directly derive logarithms with bases different to #e#, so we have to make this equation in terms of the natural log #ln#.

Using change of base, we can convert this to #y=(lnx)/(ln3)#

#1/(ln3)# is just a constant, and thus will not change.

#(dy)/(dx)=1/(ln3)*1/x->#the derivative of #lnx# is #1/x#

#=1/(xln3)#