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.

Question qty: 10
Duration in minutes: 15
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Sample questions

An algebraic result makes a logarithm argument negative. What should be done?
Does x = x satisfy log_a(x) = r?
When does log_a(f(x)) = log_a(g(x)) imply f(x) = g(x)?
Solve log_a(x) − b = 0.
Solve log_a(x + b) = log_a(c).
Hydrogen-ion concentration is h. Find pH = −log₁₀[H⁺].
Solve log_a(x + b) = r.
Solve log₁₀(x) = r.

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.

Test: Logarithmic equations

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Question Nr. 10 out of 10

Sample questions

Logarithmic equations

Solution strategy

Test: Logarithmic equations

Question Nr. 1 out of 10

Question Nr. 2 out of 10

Question Nr. 3 out of 10

Question Nr. 4 out of 10

Question Nr. 5 out of 10

Question Nr. 6 out of 10

Question Nr. 7 out of 10

Question Nr. 8 out of 10

Question Nr. 9 out of 10

Question Nr. 10 out of 10

Sample questions

Logarithmic equations

Solution strategy

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