Thread: Logarithmic Differentation

Any help with solving this... I can't figure it out.

$\displaystyle 3^xlog_8(x)$

That is, I need to find the derivative. I think this is the first step:

$\displaystyle ln(3)/ln(8) $

$\displaystyle 3^x \log_8 x = \frac{3^x \ln x}{\ln 8}$

Do i continue with using the quetient rule. Is f'(x)= $\displaystyle 3^xln(x)*3$?

Originally Posted by cjmac87

Do i continue with using the quetient rule. Is f'(x)= $\displaystyle 3^xln(x)*3$?

$\displaystyle \frac{3^x \ln{x}}{\ln{8}} = \frac{1}{\ln{8}} \cdot 3^x \ln{x}
$

use the product rule ...

$\displaystyle \frac{1}{\ln{8}}\left(3^x \cdot \frac{1}{x} + 3^x \cdot \ln{3} \cdot \ln{x}\right)$

now clean up the algebra.