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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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