Question

Find the derivative of 3/log8(x)

Answer 1

\[\large \frac{d}{dx}\frac{3}{\log_8x}\]

So we'll want to start by using our change of base formula.
\[\large \log_a(b)=\frac{\log_c(b)}{\log_c(a)}\]Where \(\large c\) is any new base value that we want it to be. In this problem we're going to let \(\large c=e\). This corresponds to the natural log, and is easy to take a derivative of.\[\large \log_a(b)=\frac{\ln b}{\ln a}\]

Answer 2

Applying this to the problem gives,
\[\large \frac{d}{dx}\frac{3}{\log_8x} \qquad = \qquad \frac{d}{dx}\frac{3}{\left(\dfrac{\ln x}{\ln 8}\right)}\]
Understand how I applied that rule?
No derivative has been taken yet. Just steps that will make the process easier.

Answer 3

Ohh okay that's why I wasn't getting it. Thanks for the start(:

Answer 4

Cool c: Lemme know if you're still stuck.