Question

Let g(x) = log7 (x),
find g ¹(0)

Answer 1

Explanation:

The derivative of log is

`(d)/(dx) ( log_(a)(x) ) = (1)/(x \: ln(a) )`

You can easily derive this using the Change of base rule, and natural log rules

`log_(a)(x) = ( log_(e)(x) )/( log_(e)(a) ) = ( ln(x) )/( ln(a) )`

Next, we differentiate with respect to x.

`(d)/(dx) ( ln(x) )/( ln(a) ) = (1)/( ln(a) ) * (d)/(dx) ln(x)`

`= (1)/(x ln(a) )`

So back to the topic at hand,.

a=7, so we get

`(1)/(x ln(7) )`

We plug in 0, we would get undefined