Q. Which of the following is the correct simplification of log_5(25) - log_5(5)?
Solution
log_5(25) = 2 and log_5(5) = 1, thus log_5(25) - log_5(5) = 2 - 1 = 1.
Correct Answer:
A
— 1
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Q. Which of the following is the correct simplification of log_a(b^2)?
-
A.
2 log_a(b)
-
B.
log_a(2b)
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C.
log_a(b) + 2
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D.
log_a(b) - 2
Solution
Using the power rule of logarithms, log_a(b^2) simplifies to 2 log_a(b).
Correct Answer:
A
— 2 log_a(b)
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Q. Which of the following is the correct simplification of log_a(b^c)?
-
A.
c * log_a(b)
-
B.
log_a(c) * log_a(b)
-
C.
log_a(b) / c
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D.
log_a(c^b)
Solution
The property of logarithms states that log_a(b^c) = c * log_a(b).
Correct Answer:
A
— c * log_a(b)
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Q. Which of the following logarithmic expressions is equivalent to log_10(0.01)?
Solution
Since 0.01 is 10^-2, log_10(0.01) = -2.
Correct Answer:
A
— -2
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Q. Which of the following logarithmic expressions is equivalent to log_2(8) - log_2(4)?
-
A.
log_2(2)
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B.
log_2(1)
-
C.
log_2(0)
-
D.
log_2(3)
Solution
Using the property of logarithms that states log_a(b) - log_a(c) = log_a(b/c), we find log_2(8) - log_2(4) = log_2(8/4) = log_2(2).
Correct Answer:
A
— log_2(2)
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Q. Which of the following logarithmic expressions is equivalent to log_3(81)?
Solution
Since 81 is 3^4, log_3(81) equals 4.
Correct Answer:
A
— 4
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Q. Which of the following logarithmic expressions is undefined?
-
A.
log_5(0)
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B.
log_5(1)
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C.
log_5(5)
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D.
log_5(25)
Solution
Logarithm of zero is undefined, hence log_5(0) is the correct answer.
Correct Answer:
A
— log_5(0)
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Q. Which of the following logarithmic identities is incorrect?
-
A.
log_a(b) + log_a(c) = log_a(bc)
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B.
log_a(b/c) = log_a(b) - log_a(c)
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C.
log_a(b^c) = c * log_a(b)
-
D.
log_a(b) * log_a(c) = log_a(bc)
Solution
The last identity is incorrect; it should be log_a(b) + log_a(c) = log_a(bc).
Correct Answer:
D
— log_a(b) * log_a(c) = log_a(bc)
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Q. Which of the following logarithmic properties is used to simplify log_a(b^c)?
-
A.
Power Rule
-
B.
Product Rule
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C.
Quotient Rule
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D.
Change of Base Formula
Solution
The Power Rule states that log_a(b^c) = c * log_a(b).
Correct Answer:
A
— Power Rule
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Q. Which of the following represents the change of base formula for logarithms?
-
A.
log_a(b) = log_c(b) / log_c(a)
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B.
log_a(b) = log_c(a) / log_c(b)
-
C.
log_a(b) = log_c(b) * log_c(a)
-
D.
log_a(b) = log_c(a) + log_c(b)
Solution
The change of base formula states that log_a(b) can be expressed as log_c(b) divided by log_c(a).
Correct Answer:
A
— log_a(b) = log_c(b) / log_c(a)
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