Question

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

Answer 1

`(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)`