Solving Logarithmic Equations Worksheet with Answer Key

What's on the worksheet

1. Solve each equation with exact answers, writing the domain and rejecting any candidate.
   \log_7(x + 1) + \log_7(x - 5) = 1\ln(x + 2) - \ln(x - 1) = \ln 4\log_3 x + \log_3(x + 2) = \log_3(4x + 15)\log_5(x - 4) + \log_5(x + 4) = 2
2. For each pair, give the domain of each expression and see what a law of logs changes.
   \log x + \log(x - 3) and \log\big(x(x - 3)\big)\ln(x + 2) - \ln(x - 1) and \ln \dfrac{x + 2}{x - 1}2\log_2 x and \log_2\left(x^2\right)\log_3(x - 4) + \log_3(6 - x) and \log_3\big((x - 4)(6 - x)\big)
3. Find k so that x equals 3 solves the equation, then solve with that k.
4. Find the step where Jasmine's solution of a log equation goes wrong.
5. Explain how an equation of two added logs is solved by condensing and why a check is needed.