How do you find the derivative of log functions of different bases?

Author Question: How do you find the derivative of log functions of different bases? (Read 1227 times)

j_sun

Sr. Member
Posts: 384

on: Jun 19, 2013

For example, what is the derivative of y = log@5(log@2x), where @ = "base"? Please show the steps.. I don't need an answer.

federox

Sr. Member
Posts: 308

Reply #1 on: Jun 19, 2013

I will demonstrate how to get the derivative of a logarithm in a base other than e, and you can do the rest.

y = log7(x) is the same as 7^y = x.

take the natural log of both sides and get: y * ln(7) = ln(x)

solve for y: y = ln(x)/ln(7)

dy/dx = 1/(x * ln(7))

use the chain rule to solve your function.

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