Properties of Logarithms Answers
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1
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Which expression is equivalent to ?
A
4 log Subscript w Baseline StartFraction x squared Over 1296 EndFraction minus one-third log Subscript w Baseline (2 x + 8)
B
4 log Subscript w Baseline (x squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)
C
4 log Subscript w Baseline (X squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)
D
4 (log Subscript w Baseline x squared minus one-third log Subscript w Baseline (x squared + 8) minus 6)
2
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What is rewritten using the power property?
A
log Subscript 15 Baseline 5
B
log Subscript 15 Baseline 6
C
2 log Subscript 15 Baseline 3
D
3 log Subscript 15 Baseline 2
3
What is written as a single logarithm?
A
log Subscript 3 Baseline 2 z
B
log Subscript 3 Baseline 2 z squared
C
log Subscript 3 Baseline StartFraction z squared Over 4 EndFraction
D
log Subscript 3 Baseline StartStartFraction 64 z squared Over StartFraction 81 OverOver 49 EndEndFraction
4
Given and , what is ?
A
1.404B
1.739C
2.773D
2.9885
The table shows a student’s proof of the quotient rule for logarithms.Let M = bx and N = by for some real numbers x and y. StepReason1Given2Substitution3Properties of logarithms4Logarithm property logb(bc) = c5SubstitutionWhat is the error in the proof?
A
The error is in step 3. The reason should be the quotient property of exponents.B
The error is in step 3. You cannot use a property of logarithms to prove that same property.C
The error is in step 2. The reason should be the quotient property of exponents.D
The error is in step 5. The student did not convert from exponential to logarithmic form correctly when solving for x and y.6
Which expression is equivalent to ?
A
4 log Subscript w Baseline StartFraction x squared Over 1296 EndFraction minus one-third log Subscript w Baseline (2 x + 8)B
4 log Subscript w Baseline (x squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)C
4 log Subscript w Baseline (X squared minus 6) minus one-third log Subscript w Baseline (x squared + 8)D
4 (log Subscript w Baseline x squared minus one-third log Subscript w Baseline (x squared + 8) minus 6)7
What is written as a single logarithm?
A
log Subscript 3 Baseline 2 zB
log Subscript 3 Baseline 2 z squaredC
log Subscript 3 Baseline StartFraction z squared Over 4 EndFractionD
log Subscript 3 Baseline StartStartFraction 64 z squared Over StartFraction 81 OverOver 49 EndEndFraction8
Which expression is equivalent to ?
A
log Subscript 8 Baseline 4 + log Subscript 8 Baseline a minus log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c
B
log Subscript 8 Baseline 4 + log Subscript 8 Baseline a + (log Subscript 8 Baseline (b minus 4) minus 4 log Subscript 8 Baseline c)
C
log Subscript 8 Baseline 4 a + log Subscript 8 Baseline b minus 4 minus 4 log Subscript 8 Baseline c minus 4
D
log Subscript 8 Baseline 4 + log Subscript 8 Baseline a minus log Subscript 8 Baseline (b minus 4) minus log Subscript 8 Baseline 4 c
9
Sam is proving the product property of logarithms. StepJustificationGivenSubstitution Which expression and justification completes the third step of her proof?
A
; power rule of exponents
B
subtraction property of exponents
C
multiplication rule of exponents
D
division property of exponents
10
Which expression is equivalent to log3(x + 4)?
A
log3 – log(x + 4)B
log12 + logxC
log3 + log(x + 4)D
StartFraction log 3 Over log (x + 4) EndFraction
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