Test
Logarithmic equations
This test focuses on solving several types of logarithmic equations. Tasks apply logarithm properties and the fundamental identity, establish domain restrictions and reject invalid solutions.
Time left: 00:00:00
Sample questions
- Solve log___(x + ___) = ___.
- Solve log___(x + ___) = log___(___).
- Solve log___(x) − ___ = 0.
- An algebraic result makes a logarithm argument negative. What should be done?
- Hydrogen-ion concentration is ___. Find pH = −log₁₀[H⁺].
Logarithmic equations
Every logarithm argument must be positive, and its base must be positive and different from one. Record these conditions before transforming the equation.
Solution strategy
Use logarithm rules to combine a sum into the logarithm of a product and a difference into that of a quotient. Equal logarithms with the same base have equal arguments. After solving the resulting algebraic equation, reject every value violating positivity of any original argument.
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