Algebra
# Exponential Functions

If $3^n = 5$ and $4^m = 8$, what is the value of $\large 9^{n+m} ?$

Let $f(x) = \left( \dfrac12 \right)^{x-5} - 64,$ and suppose that the graphs of $y = |f(x)|$ and $y=k$ meet in the first quadrant.

Find the number of all the positive integers $k$ that satisfy the above condition.

What is the sum of all possible integer values of $x$ such that

$\large (x^2-55x+755)^{(x^2-62x+936 )} =1 ?$

Solve for $x$:

$3 = 4^x + 5^x + 6^x$