7
QuizMultiple Choice

Evaluating Logarithmic Expressions

Question 7 • FL-1200330-Algebra 2 CR

A Cepheid star is a type of variable star, which means its brightness is not constant. The relationship between the brightness of a Cepheid star and its period, or length of its pulse, is given by M = –2.78(log P) – 1.35, where M is the absolute magnitude, or brightness, of the star, and P is the number of days required for the star to complete one cycle. What is the absolute magnitude of a star that has a period of 45 days? Use a calculator. Round your answer to the nearest hundredth.

Answer
A
–5.95
B
–4.60
C
3.25
D
4.60

Explanation

Substitute P = 45 into the formula: M = −2.78(log 45) − 1.35. Using log base 10, log 45 ≈ 1.6532, so M ≈ −2.78(1.6532) − 1.35 ≈ −5.95. The absolute magnitude is −5.95, choice A.

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