Problem preview

F-LE.4.3 Warmup M3-032-A08-V02

Use logarithm properties to simplify numeric logarithmic expressions and estimate values.

Approximate a numeric logarithm by change of base to stated precision

Problem

Evaluate \(\log_{4}(11)\) by change of base. Give the quotient, the value rounded to \(\text{four}~\text{decimal}~\text{places}\), and a benchmark-power check.

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Candidate analysis: ln(11)/ln(4) ≈ 1.7298. Since 4 < 11 < 16, the value must lie between 1 and 2.

Candidate analysis: Using ln(11) ≈ 2.4 and ln(4) ≈ 1.4 gives 2.4/1.4 ≈ 1.7143. Since 4 < 11 < 16, the value lies between 1 and 2.

Candidate analysis: ln(11)/ln(4) ≈ 1.7297. Since 4 < 11 < 16, the value must lie between 1 and 2.

Candidate analysis: ln(4)/ln(11) ≈ 0.5781. Since 1 < 4 < 11, this reciprocal lies between 0 and 1.

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Curriculum context

Course: Math III
Standard: F-LE.4.3
Category: Functions
Domain: Linear, Quadratic, and Exponential Models
Objective: Use logarithm properties to simplify numeric logarithmic expressions and estimate values.
Problem type: Approximate a numeric logarithm by change of base to stated precision