Find log₂(32).
Incorrect answer: 16
A logarithm can be negative even though its argument must be positive. log₁₀(0.01) is −2, but log₁₀(−2) is not defined in the real numbers.
Treating a logarithm as division
A logarithm asks for an exponent. Rewrite the statement as a power of the base.
The correction
5
2⁵ = 32.
- Identify the base, argument, and unknown exponent.
- Translate log_b(a) = c into b raised to c equals a.
- Evaluate or solve, then check that every original logarithm has a positive argument.
Try the reasoning in another example
Find log₁₀(0.01).
- 0.01 is 1/100.
- 10 raised to −2 equals 1/100.
Answer: −2
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
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