Read a Logarithm as an Exponent Question

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: Evaluate log₂(4). Candidate answers: (A) 1 (B) 2 (C) 3 (D) 4.
• Independent check inputs: Evaluate log₂(8). Candidate answers: (A) 2 (B) 3 (C) 4 (D) 6.

Learn the idea

Logarithms reverse exponentiation with a valid positive base other than one. They answer exponent questions, reorganize multiplicative structure and solve exponential relationships while requiring positive real logarithm arguments. A logarithm log_b(A) asks which exponent on b yields A. When the argument is a recognizable power of the base, the value can be found exactly by that inverse relationship.

Here is the method on the supplied teaching case. A logarithm answers which exponent produces the argument. Since 2^2=4, log₂(4)=2. The argument is positive and the base is valid.

The logarithm is not division of the argument by the base. A real logarithm needs positive argument and positive base not equal to one; verify those conditions before applying a power pattern.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: Evaluate log₂(512). Candidate answers: (A) 10 (B) 18 (C) 8 (D) 9. Show the mathematical reason, not only the selected answer. Expected result: 9. A logarithm answers which exponent produces the argument. Since 2^9=512, log₂(512)=9. The argument is positive and the base is valid.

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