Question

Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

g(x) = log8 (2x - 5)

Answer 1

The derivative of the function is:

`g'(x) = (1)/(2.0794*(2x - 5))`

Explanation:

If we have a function in the following format:

`g(x) = log_a(f(x))`

This function has the following derivative

`g'(x) = (f'(x))/(f(x)*ln(a))`

In this problem, we have that:

`f(x) = log_8(2x - 5)`

So
`f(x) = 2x - 5, f'(x) = 2, a = 8`

The derivative is

`g'(x) = (f'(x))/(f(x)*ln(a))`

`g'(x) = (1)/((2x-5)*ln(8))`

`g'(x) = (1)/(2.0794*(2x - 5))`