Exponents and radicals practice
Solve six types of logarithmic equations with exact answers. Choose 12, 14 or 16 questions and check every solution in the original logarithms.
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Solve each equation over the real numbers. Give exact answers and check that every original logarithm has a positive argument.
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Choose any of six equation forms and 12, 14 or 16 questions. Use equal arguments or logarithm laws to obtain a linear or quadratic equation. Answers stay exact, including simplified square roots.
Every original logarithm must have a positive argument. The answer key checks each candidate and explains which values are excluded. A negative candidate can still be valid; test the argument rather than the sign of the variable alone.
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Learning objective
Use logarithm laws to solve linear and quadratic equations, then reject candidates outside the original domain.
Worked example
The algebraic candidates are -4 and 5. Only x = 5 is a solution.
Equal logarithms with the same base have equal positive arguments. Set 3x squared - 60 = 3x, then factor x squared - x - 20. At x = -4 both arguments are -12, so discard it. At x = 5 both arguments are 15.
Teaching notes
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Choose your options, update the preview, then download the exact same pages.
Choose equation forms and worksheet length. Keep exact answers and check the original logarithm arguments.
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