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Vadim26 [7]
1 year ago
12

Let g(x) = log7 (x), find g ¹(0)

Mathematics
1 answer:
klasskru [66]1 year ago
6 0

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

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