Q. If log_a(5) = p and log_a(25) = q, what is the relationship between p and q?
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A.
q = 2p
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B.
q = p/2
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C.
q = p^2
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D.
q = p + 1
Solution
log_a(25) = log_a(5^2) = 2 log_a(5) = 2p, hence q = 2p.
Correct Answer: A — q = 2p
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Q. If log_a(b) = p and log_a(c) = q, then log_a(bc) is equal to?
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A.
p + q
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B.
pq
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C.
p - q
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D.
p/q
Solution
log_a(bc) = log_a(b) + log_a(c) = p + q.
Correct Answer: A — p + q
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Q. If log_a(b) = p and log_a(c) = q, what is log_a(bc)?
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A.
p + q
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B.
pq
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C.
p - q
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D.
p/q
Solution
log_a(bc) = log_a(b) + log_a(c) = p + q.
Correct Answer: A — p + q
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Q. If log_b(27) = 3, what is the value of b?
Solution
log_b(27) = 3 implies b^3 = 27 => b = 3.
Correct Answer: A — 3
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Q. If log_x(16) = 4, what is the value of x?
Solution
log_x(16) = 4 implies x^4 = 16 => x^4 = 2^4 => x = 2.
Correct Answer: B — 4
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Q. If log_x(27) = 3, find x.
Solution
log_x(27) = 3 implies x^3 = 27 => x = 3.
Correct Answer: B — 9
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Q. If log_x(4) = 2, what is the value of x?
Solution
log_x(4) = 2 implies x^2 = 4 => x = 2.
Correct Answer: C — 8
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Q. If log_x(81) = 4, find x.
Solution
log_x(81) = 4 implies x^4 = 81 => x^4 = 3^4 => x = 3.
Correct Answer: A — 3
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Q. If log_x(81) = 4, what is the value of x?
Solution
log_x(81) = 4 implies x^4 = 81 => x = 3.
Correct Answer: A — 3
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Q. Solve for x: log_3(x + 1) - log_3(x - 1) = 1.
Solution
Using properties of logarithms, log_3((x + 1)/(x - 1)) = 1 => (x + 1)/(x - 1) = 3 => x + 1 = 3(x - 1) => x = 2.
Correct Answer: A — 2
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Q. Solve for x: log_3(x) = 2.
Solution
log_3(x) = 2 implies x = 3^2 = 9.
Correct Answer: B — 9
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Q. Solve for x: log_5(x + 1) - log_5(x - 1) = 1.
Solution
Using properties of logarithms: log_5((x + 1)/(x - 1)) = 1 => (x + 1)/(x - 1) = 5 => x + 1 = 5(x - 1) => 4x = 6 => x = 2.
Correct Answer: A — 2
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Q. Solve for x: log_5(x) = 2.
Solution
log_5(x) = 2 implies x = 5^2 = 25.
Correct Answer: C — 25
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Q. What is the value of log_10(1000) + log_10(0.01)?
Solution
log_10(1000) = 3 and log_10(0.01) = -2, thus 3 - 2 = 1.
Correct Answer: C — -1
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Q. What is the value of log_10(1000)?
Solution
log_10(1000) = log_10(10^3) = 3.
Correct Answer: C — 3
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Q. What is the value of log_2(32) - log_2(4)?
Solution
log_2(32) = 5 and log_2(4) = 2. Therefore, 5 - 2 = 3.
Correct Answer: C — 3
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Q. What is the value of log_2(32) - log_2(8)?
Solution
log_2(32) = 5 and log_2(8) = 3. Therefore, 5 - 3 = 2.
Correct Answer: C — 3
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Q. What is the value of log_3(27) - log_3(9)?
Solution
log_3(27) = 3 and log_3(9) = 2. Therefore, 3 - 2 = 1.
Correct Answer: B — 1
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Q. What is the value of log_3(81)?
Solution
log_3(81) = log_3(3^4) = 4.
Correct Answer: C — 4
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Q. What is the value of log_4(64)?
Solution
log_4(64) = log_4(4^3) = 3.
Correct Answer: D — 5
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Q. What is the value of log_5(125)?
Solution
log_5(125) = log_5(5^3) = 3.
Correct Answer: B — 3
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Q. What is the value of log_5(25) - log_5(5)?
Solution
log_5(25) = 2 and log_5(5) = 1. Therefore, 2 - 1 = 1.
Correct Answer: A — 1
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Q. Which of the following is equivalent to log_a(b^c)?
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A.
c * log_a(b)
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B.
log_a(b) / c
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C.
log_a(c) + log_a(b)
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D.
log_a(b) - c
Solution
log_a(b^c) = c * log_a(b) by the power rule of logarithms.
Correct Answer: A — c * log_a(b)
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