AnswersFL-1200330-Algebra 2 CREvaluating Logarithmic Expressions

Evaluating Logarithmic Expressions Answers

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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.

A
–5.95
B
–4.60
C
3.25
D
4.60
23

The magnitude, M, of an earthquake is defined to be , where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. Which equation represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake?

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A
M = log StartFraction I Over S EndFraction
Option A
B
M = log (10 S)
Option B
C
M = log StartFraction 10 S Over S EndFraction
Option C
D
M = log StartFraction 10 Over S EndFraction
Option D
24

Which equation has x = –6 as the solution?

A
log Subscript x Baseline 36 = 2
Option A
B
log Subscript 3 Baseline (2 x minus 9) = 3
Option B
C
log Subscript 3 Baseline 216 = x
Option C
D
log Subscript 3 Baseline (negative 2 x minus 3) = 2
Option D
25

What is the value of ?

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A
–6
B
–2
C
2
D
6

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