Question

Let g(x) = log7 (x),
find g ¹(0)

Answer 1

Step-by-step explanation:

The derivative of log is

$\frac{d}{dx} ( log_{a}(x) ) = \frac{1}{x \: ln(a) }$

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

$log_{a}(x) = \frac{ log_{e}(x) }{ log_{e}(a) } = \frac{ ln(x) }{ ln(a) }$

Next, we differentiate with respect to x.

$\frac{d}{dx} \frac{ ln(x) }{ ln(a) } = \frac{1}{ ln(a) } \times \frac{d}{dx} ln(x)$

$= \frac{1}{x ln(a) }$

So back to the topic at hand,.

a=7, so we get

$\frac{1}{x ln(7) }$

We plug in 0, we would get undefined