1. ## logarithms equation

how do you prove that? (see the image)
how would you simplify the left side to show it equals the right?

2. ## Re: logarithms equation

Hint: $\log_a b \times \log _b a = 1$, so $\frac 1 {\log _a b} = \log _b a$

3. ## Re: logarithms equation

Originally Posted by rgchel
how do you prove that? (see the image)
how would you simplify the left side to show it equals the right?
Here is a second way of looking at it.

Because $\log_b(x)=\dfrac{\log(x)}{\log(b)}$ then $(\log_3(x))^{-1}=\dfrac{\log(3)}{\log(x)}$

Now on the LHS we have a common denominator.