Solving Exponential Equations by Matching Bases Worksheet with Answer Key

What's on the worksheet

1. Solve each equation by writing both sides as powers of the same base.
   6^{3x - 2} = 21649^{x - 2} = 343^{x}\left(\dfrac{1}{4}\right)^{x + 2} = 32125^{x} = \dfrac{1}{\sqrt{5}}0.01^{x} = 1000^{x - 5}
2. Write each side as a single power of one base, then solve.
   \dfrac{8^{x}}{4^{x - 1}} = 2^{3x}9^{x} \cdot 27 = \sqrt[3]{3}\sqrt{2^{x}} = 4^{x - 3}
3. Get a single power on its own, then solve:
   5 \cdot 4^{x - 1} - 3 = 3173^{x + 2} - 3^{x} = \dfrac{8}{9}
4. Solve each equation, or explain why there is no real solution.
   4^{x^2} = 2^{7x - 3}\left(\dfrac{1}{5}\right)^{x^2} = 25^{x} \cdot 125
5. Word problem: the f-number of a camera lens after closing by some stops.
6. Check Mei's matching of exponents with base 1 and find every solution.
7. Explain each student's mistake, then solve correctly and check.