Find and factor the derivative of the function
f(x)= log8 (4^x +3^-x)

Question

Find and factor the derivative of the function
f(x)= log8 (4^x +3^-x)

anonymous · Answer

I am always confused when I read log8, is log8 = lg8 or ln8? 

lg has a base of 10, ln has a base of e

anonymous · Answer

I am asking this because:

$$\Large \log_8(4^x-3^{-x}) $$
Would not be the same problem as

$$ \Large \underbrace{\ln8}_{\text{a number}}(4^x-3^{-x}) $$

anonymous · Answer

he probably means log base 8. log being implied as ln is more of an advanced technique of physicists and chemists. Mathematicians wouldn't do such a thing.

anonymous · Answer

I agree @GregTheo. I keep asking nowadays because I have solved - and on top of that, caused a lot of confusion - by copying the wrong problem (-:

anonymous · Answer

@pdube 

Is it the logarithm base eight? 

$$\Large \log_8x $$

anonymous · Answer

yes ...sorry I took awhile to reply I lost connection

anonymous · Answer

I think I got it but I'm not sure if I got the derivative right

anonymous · Answer

No problem, well clearly what you have to do first is to use change of bases

$$\Large \log_8x= \frac{\ln x}{\ln8} $$

So you can substitute that back in for your function and you will get:

$$\Large \frac{1}{\ln8} \cdot \ln (4^x-3^{-x})$$