Logarithms
Q. If log_2(x) + log_2(4) = 6, what is the value of x?
Solution
log_2(x) + 2 = 6 implies log_2(x) = 4, so x = 2^4 = 16.
Correct Answer: C — 32
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Q. If log_3(x) = 4, what is the value of x?
-
A.
27
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B.
81
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C.
243
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D.
729
Solution
log_3(x) = 4 implies x = 3^4 = 81.
Correct Answer: C — 243
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Q. If log_4(256) = x, what is the value of x? (2022)
Solution
log_4(256) = log_4(4^4) = 4.
Correct Answer: D — 8
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Q. If log_a(16) = 4, what is the value of a? (2021)
Solution
log_a(16) = 4 implies a^4 = 16. Since 16 = 2^4, we have a^4 = 2^4, thus a = 2.
Correct Answer: A — 2
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Q. If log_b(25) = 2, what is the value of b?
Solution
log_b(25) = 2 implies b^2 = 25. Therefore, b = 5.
Correct Answer: A — 5
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Q. If log_x(64) = 6, what is the value of x? (2023)
Solution
log_x(64) = 6 implies x^6 = 64. Since 64 = 2^6, we have x = 2.
Correct Answer: C — 8
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Q. What is the value of log_10(0.01)?
Solution
log_10(0.01) = log_10(10^-2) = -2.
Correct Answer: B — -2
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Q. What is the value of log_2(1/8)? (2023)
Solution
log_2(1/8) = log_2(2^-3) = -3.
Correct Answer: A — -3
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Q. What is the value of log_5(1)?
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A.
0
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B.
1
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C.
5
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D.
undefined
Solution
log_5(1) = 0 because 5^0 = 1.
Correct Answer: A — 0
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Q. Which of the following is equal to log_10(0.01)? (2019)
Solution
log_10(0.01) = log_10(10^-2) = -2.
Correct Answer: B — -2
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Q. Which of the following is equivalent to log_2(32)?
Solution
log_2(32) = log_2(2^5) = 5.
Correct Answer: B — 5
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Q. Which of the following is true for log_a(bc)?
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A.
log_a(b) + log_a(c)
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B.
log_a(b) - log_a(c)
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C.
log_a(bc) = log_a(b) * log_a(c)
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D.
None of the above
Solution
log_a(bc) = log_a(b) + log_a(c) by the product rule of logarithms.
Correct Answer: A — log_a(b) + log_a(c)
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