Solving by Taking a Logarithm of Both Sides Worksheet with Answer Key

What's on the worksheet

1. Solve each equation, giving the exact answer and its value to three decimal places.
   \left(\dfrac{3}{2}\right)^{x} = 1010^{x + 1} = 0.650.5^{x} = 12
2. Isolate the power, then solve, or show there is no solution.
   9 - 2 \cdot 5^{x} = 153(1.2)^{x - 4} = 7.520 - 3e^{-0.5x} = 14
3. Solve by taking a logarithm of both sides and write the exact answer as one fraction.
   3^{x + 1} = 2 \cdot 5^{x}e^{x - 1} = 10^{x}
4. Word problem: how many years until a college's tuition doubles at 4% a year.
5. Word problem: weekly sales of a new album as they fall each week.
6. Word problem: how many sheets of tinted window film let through a set share of light.
7. Say what went wrong in each student's work before taking logs, then solve correctly.