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  1. Subjects ›
  2. College Algebra ›
  3. Question of the Day

College Algebra Question of the Day

College Algebra Question of the Day

Answer today's College Algebra question, reveal the full explanation, then keep the streak going with a new question every day.

A scientific calculator displays log⁡2(50)≈5.644\log_2(50) \approx 5.644log2​(50)≈5.644. Using this information and the change of base formula, what is the approximate value of log⁡50(2)\log_{50}(2)log50​(2)?

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Question of the Day

A scientific calculator displays log⁡2(50)≈5.644\log_2(50) \approx 5.644log2​(50)≈5.644. Using this information and the change of base formula, what is the approximate value of log⁡50(2)\log_{50}(2)log50​(2)?

  1. 0.1770.1770.177 (correct answer)
  2. −5.644-5.644−5.644
  3. 5.6445.6445.644
  4. 0.6440.6440.644

Explanation: Using the change of base formula, log⁡50(2)=log⁡2(2)log⁡2(50)=1log⁡2(50)=15.644≈0.177\log_{50}(2) = \frac{\log_2(2)}{\log_2(50)} = \frac{1}{\log_2(50)} = \frac{1}{5.644} \approx 0.177log50​(2)=log2​(50)log2​(2)​=log2​(50)1​=5.6441​≈0.177. This demonstrates that log⁡a(b)\log_a(b)loga​(b) and log⁡b(a)\log_b(a)logb​(a) are reciprocals when both are positive. Choice B would be incorrect as it suggests a negative logarithm when both base and argument are greater than 1. Choice C incorrectly assumes the logarithms are equal. Choice D appears to subtract 5 from 5.644, which has no mathematical basis.