Evaluating Logarithmic Expressions

Question 1

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.

Revolt · Accepted Answer

–5.95

Question 2

What is the value of ?

Revolt · Accepted Answer

2

Question 3

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?

Revolt · Accepted Answer

M = log StartFraction 10 S Over S EndFraction

Question 4

What is the value of log 43? Use the calculator. Round your answer to the nearest tenth.

Revolt · Accepted Answer

1.6

Question 5

Which logarithmic equation is equivalent to 32 = 9?

Revolt · Accepted Answer

2 = log Subscript 3 Baseline 9

Question 6

What is the solution of ?

Revolt · Accepted Answer

2

Question 7

What is the solution of ?

Revolt · Accepted Answer

4

Question 8

What is the value of ?

Revolt · Accepted Answer

–2

Question 9

What is the value of log 13? Use a calculator. Round your answer to the nearest tenth.

Revolt · Accepted Answer

1.1

Question 10

Which equation has x = –6 as the solution?

Revolt · Accepted Answer

log Subscript 3 Baseline (negative 2 x minus 3) = 2

Evaluating Logarithmic Expressions Answers

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