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## Exponential Functions

From compound interest to bubonic plague, things that grow or spread really fast are often modeled by exponential functions. Learn about these powerful functions (pun intended?).

# Exponential Equations

Given $$9^a = 27^{10}$$, where $$a$$ is a positive integer, what is the value of $$a$$?

How many real values of $$x$$ satisfy the following equation $$9^x - 6 \cdot 3^x - 55 = 0$$?

What is the sum of the absolute values of all the $$x$$'s that satisfy the equation $(2+\sqrt{3})^x+(2-\sqrt{3})^x=4?$

$$x$$ and $$y$$ are real numbers that satisfy $$45y = 81^x$$ and $$5y = 3^{x + 64}$$. What is the value of $$x$$?

Solve for $$x$$

$5 ^ x + 5 ^{x-1} + 5 ^ {x-2} = 3875 .$

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