Question

How do you find the derivative of `log_7x`?

Answer 1

Rewrite the expression using the change of base formula.

`log_7x=lnx/ln7`

This is simple to differentiate. The only tricky thing is to remember that `1/ln7` is a constant, so it can be brought outside when differentiating:

`d/dx(lnx/ln7)=1/ln7*d/dx(lnx)`

Since `d/dx(lnx)=1/x`,

`d/dx(lnx/ln7)=1/ln7(1/x)=color(red)(1/(xln7)`