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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?).

Rules of Exponents - Algebraic

         

If \( 3 ^ N = 3 ^ 5 \times 3 ^ 4\), what is the value of \(N\)?

What value of \(N\) satisfies the equation

\[ \frac { 8 ^ {22}} { 8 ^ {11}} = 8 ^ N? \]

Given \(3^N = 9 ^{10} \), what is the value of \(N\)?

Hint: Rewrite 9 as \(3^2.\)

If \(x\) is a real number satisfying \( 14 ^x = 3 \), what is the value of \( 14 ^{2x + 1} ?\)

\(x\) and \(y\) satisfy \(2^x = 10\) and \(10 ^ y = 128\). What is the value of \(xy\)?

Hint: Rewrite the "10" in \(10^y = 128\) by using the fact that \(2^x = 10.\)

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