Properties of Logarithms

Question 1

Which expression is equivalent to ?

Revolt · Accepted Answer

C: 4 log Subscript w Baseline (X squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)

Question 2

Given and , what is ?

Revolt · Accepted Answer

A: 1.404

Question 3

The proof for the power property of logarithms appears in the table with an expression missing. StepReasonGivenSubstitution Properties of exponentsLogarithm property SubstitutionCommutative property of multiplicationWhich expression is missing from the proof?

Revolt · Accepted Answer

C: mc027-9.jpg

Question 4

Which expression is equivalent to ?

Revolt · Accepted Answer

C: log Subscript 3 Baseline c minus log Subscript 3 Baseline (9)

Question 5

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as , where and is the least intense sound a human ear can hear. Brandon is trying to take a nap, and he can barely hear his neighbor mowing the lawn. The sound intensity level that Brandon can hear is 10-10. Ahmad, Brandon’s neighbor that lives across the street, is mowing the lawn, and the sound intensity level of the mower is 10-4. How does Brandon’s sound intensity level compare to Ahmad’s mower?

Revolt · Accepted Answer

A: Brandon’s sound intensity is the level of Ahmad’s mower.

Question 6

Given and , what is ?

Revolt · Accepted Answer

C: 2.402

Question 7

What is written as a single logarithm?

Revolt · Accepted Answer

B: log Subscript 5 Baseline (25 x Superscript 6 Baseline) RootIndex 3 StartRoot x squared + 6 EndRoot

Question 8

Which expression is equivalent to ?

Revolt · Accepted Answer

B: log Subscript 12 Baseline one-half minus (log Subscript 12 Baseline 8 + log Subscript 12 Baseline w)

Question 9

Sam is proving the product property of logarithms. StepJustificationGivenSubstitution Which expression and justification completes the third step of her proof?

Revolt · Accepted Answer

C: multiplication rule of exponents

Question 10

When proving the product, quotient, or power rule of logarithms, various properties of logarithms and exponents must be used. Which property listed below is used in all of these proofs?

Revolt · Accepted Answer

D: mc029-4.jpg

Properties of Logarithms Answers

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