How do you find the derivative of #f(x)=Log_5(x)#?

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Answer 1 · 2016-07-22T19:48:57

#1/(xln(5))#

We want to get this into natural logs as we know how to differentiate them.

#y = log_5x#

#5^y = x#

#ln(x) = ln(5^y)#

#ln(x) = yln(5) implies y = ln(x)/ln(5)#

So now we have to find

#d/(dx) ((ln(x))/(ln(5)))#

#= 1/(ln(5)) d/(dx)(ln(x))#

#= 1/(ln(5)) * 1/x = 1/(xln(5))#