# Thread: Differentiating and simplifying logarithmic functions.

1. ## Differentiating and simplifying logarithmic functions.

For a) I am supposed to use logarithmic differentiation to find the derivative.

For b) I am supposed to simplify it.

How would I do these? I have been able to do other hw problems however for these exact ones there are no examples to follow in the book

2. ## Re: Differentiating and simplifying logarithmic functions.

For a)

Assume we have $y=3^x$
Take natural logs of both sides:
$ln(y)=x\cdot{ln(3)}$
Now you can use implicit differentiation on both sides.

Edit: For you, things aren't *quite* as simple - but using a simple substitution will help put things into a similar form.

For b)

$(\frac{1}{4})^x=4^{-x}$

$16^\frac{x}{2}=(4^2)^{\frac{x}{2}}$

Tidy up with your exponent laws.