Find the $r$ that satisfies $\log_{16} (r+16) = \frac{5}{4}$.
To solve for $r$, I need to get rid of the logarithm on the left side. One way to do that is to use the exponent rule of logarithms, which says that $\log_b x = y$ if and only if $b^y = x$. In this case, that means I can rewrite the equation as $16^{\frac{5}{4}} = r+16$. Now I have an equation without logarithms, but I still need to isolate $r$. So, $16^{\frac{5}{4}} = (2^4)^{\frac{5}{4}} = 2^{4 \cdot \frac{5}{4}} = 2^5 = 32$. Now the equation becomes $32 = r+16$. To isolate $r$, I can subtract 16 from both sides, which gives me $16 = r$. This is the final answer. 