Q. If log_3(x) = 4, what is the value of x?
-
A.
27
-
B.
81
-
C.
243
-
D.
729
Solution
log_3(x) = 4 implies x = 3^4 = 81.
Correct Answer: C — 243
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Q. If log_4(16) = x, what is the value of x?
Solution
log_4(16) = log_4(4^2) = 2.
Correct Answer: B — 2
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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_4(64) = x, what is the value of x?
Solution
log_4(64) = log_4(4^3) = 3.
Correct Answer: B — 3
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Q. If log_4(x) = 1/2, what is the value of x?
Solution
log_4(x) = 1/2 implies x = 4^(1/2) = 2.
Correct Answer: A — 2
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Q. If log_4(x) = 2, what is the value of x?
Solution
log_4(x) = 2 implies x = 4^2 = 16.
Correct Answer: C — 16
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Q. If log_4(x) = 3, find x.
-
A.
16
-
B.
64
-
C.
256
-
D.
1024
Solution
log_4(x) = 3 implies x = 4^3 = 64.
Correct Answer: B — 64
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Q. If log_4(x) = 3, what is the value of x?
-
A.
16
-
B.
64
-
C.
256
-
D.
1024
Solution
log_4(x) = 3 implies x = 4^3 = 64.
Correct Answer: B — 64
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Q. If log_5(25) + log_5(5) = x, what is the value of x?
Solution
log_5(25) = 2 and log_5(5) = 1. Therefore, x = 2 + 1 = 3.
Correct Answer: C — 3
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Q. If log_5(25) = x, then what is the value of log_5(125) in terms of x?
-
A.
x + 1
-
B.
2x
-
C.
3x
-
D.
x - 1
Solution
log_5(125) = log_5(5^3) = 3. Since log_5(25) = 2, we have x = 2, thus log_5(125) = 3.
Correct Answer: C — 3x
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Q. If log_5(25) = x, what is the value of log_5(5^x)?
Q. If log_5(25) = x, what is the value of x?
Solution
log_5(25) = log_5(5^2) = 2.
Correct Answer: B — 2
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Q. If log_5(x) = 1/2, what is the value of x?
-
A.
5
-
B.
25
-
C.
sqrt(5)
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D.
1/5
Solution
log_5(x) = 1/2 implies x = 5^(1/2) = sqrt(5).
Correct Answer: C — sqrt(5)
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Q. If log_5(x) = 2, what is the value of x?
Solution
log_5(x) = 2 implies x = 5^2 = 25.
Correct Answer: C — 25
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Q. If log_7(49) = x, what is the value of x?
Solution
Since 49 = 7^2, log_7(49) = 2, thus x = 2.
Correct Answer: B — 2
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Q. If log_a(16) = 2, what is the value of a?
Solution
From log_a(16) = 2, we have a^2 = 16, thus a = 4.
Correct Answer: B — 4
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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_a(2) = x and log_a(3) = y, then log_a(6) is equal to?
-
A.
x + y
-
B.
xy
-
C.
x - y
-
D.
x/y
Solution
log_a(6) = log_a(2 * 3) = log_a(2) + log_a(3) = x + y.
Correct Answer: A — x + y
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Q. If log_a(2) = x and log_a(3) = y, what is log_a(6)?
-
A.
x + y
-
B.
xy
-
C.
x - y
-
D.
x/y
Solution
log_a(6) = log_a(2 * 3) = log_a(2) + log_a(3) = x + y.
Correct Answer: A — x + y
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Q. If log_a(3) = 0.5, what is the value of a? (2022)
Solution
log_a(3) = 0.5 implies a^0.5 = 3, thus a = 3^2 = 9.
Correct Answer: A — 9
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Q. If log_a(4) = 2 and log_a(16) = x, what is the value of x?
Solution
log_a(16) = log_a(4^2) = 2 * log_a(4) = 2 * 2 = 4.
Correct Answer: B — 4
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Q. If log_a(4) = 2, what is the value of a?
Solution
log_a(4) = 2 implies a^2 = 4 => a = 2.
Correct Answer: B — 4
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Q. If log_a(5) = p and log_a(25) = q, then what is the relationship between p and q?
-
A.
q = 2p
-
B.
q = p/2
-
C.
q = p^2
-
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(5) = p and log_a(25) = q, what is the relationship between p and q?
-
A.
q = 2p
-
B.
q = p/2
-
C.
q = p^2
-
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) = c, what is b in terms of a and c?
-
A.
a^c
-
B.
c^a
-
C.
a/c
-
D.
c/a
Solution
From the definition of logarithms, b = a^c.
Correct Answer: A — a^c
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Q. If log_a(b) = c, which of the following is equivalent to this expression?
-
A.
a^c = b
-
B.
b^c = a
-
C.
c^a = b
-
D.
a^b = c
Solution
The expression log_a(b) = c can be rewritten in exponential form as a^c = b.
Correct Answer: A — a^c = b
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Q. If log_a(b) = c, which of the following is equivalent?
-
A.
a^c = b
-
B.
b^c = a
-
C.
c^a = b
-
D.
b^a = c
Solution
The definition of logarithms states that if log_a(b) = c, then a raised to the power of c equals b, hence a^c = b.
Correct Answer: A — a^c = b
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Q. If log_a(b) = p and log_a(c) = q, then log_a(bc) is equal to?
-
A.
p + q
-
B.
pq
-
C.
p - q
-
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)?
-
A.
p + q
-
B.
pq
-
C.
p - q
-
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(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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