Integral calculus help please
Prove the third law of logarithms. Hint: Start by showing that both sides of the equation have the same derivative.

Question

Integral calculus help please
Prove the third law of logarithms. Hint: Start by showing that both sides of the equation have the same derivative.

anonymous · Answer

do you have an example or is it just asking you to prove it?

ranga · Answer

http://www.youtube.com/watch?v=LgeRUr8ALGI

ranga · Answer

you are welcome.

rational · Answer

I think you need to use mean value theorem

rational · Answer

say
$f(x) =  \ln  (x^r)$  and    $g(x) = r \ln (x)$

$f'(x) =  \dfrac{1}{x^r} rx^{r-1} =  \dfrac{r}{x}$

$g'(x) =  \dfrac{r}{x}$

That means $f'(x) =  g'(x)$

rational · Answer

thats the first step only ^

rational · Answer

Any idea how to conclude ?

ranga · Answer

Hint: Start by showing that both sides of the equation have the same derivative.
Didn't read the full question!  @rational is correct.