Question

How do you differentiate `log_2(3x-1)`?

Answer 1

`3/((3x-1)*ln2)`

Explanation:

For this problem, the following formula will be used

`color(white)(aaaaaaaaaaa)` `color(green)(d/dxlog_a[f(x)] = 1/(f(x)*lna) *f'(x)`

What this basically means, is that the derivative of a log base a of some function equals 1 over that function times the natural log of base a times the derivative of `f(x)`.

• `d/dxlog_2(3x-1)`

• `=1/((3x-1)*ln2)*3`

• `=3/((3x-1)*ln2)`