Q. If log_10(2) = a, what is log_10(20) in terms of a?
-
A.
2a
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B.
a + 1
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C.
a + 2
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D.
2 + a
Solution
log_10(20) = log_10(2 * 10) = log_10(2) + log_10(10) = a + 1.
Correct Answer: B — a + 1
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Q. If log_10(x) = 2, what is the value of x?
-
A.
100
-
B.
200
-
C.
300
-
D.
400
Solution
log_10(x) = 2 implies x = 10^2 = 100.
Correct Answer: A — 100
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Q. If log_2(x + 1) - log_2(x) = 1, what is the value of x?
Solution
log_2((x + 1)/x) = 1 implies (x + 1)/x = 2 => x + 1 = 2x => x = 1.
Correct Answer: A — 1
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Q. If log_2(x + 1) = 3, what is the value of x?
Solution
log_2(x + 1) = 3 implies x + 1 = 2^3 = 8 => x = 7.
Correct Answer: A — 6
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Q. If log_2(x) + log_2(4) = 5, find x.
Solution
log_2(x) + 2 = 5 => log_2(x) = 3 => x = 2^3 = 8.
Correct Answer: B — 32
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Q. If log_2(x) + log_2(x - 3) = 3, what is the value of x?
Solution
log_2(x(x - 3)) = 3 => x(x - 3) = 2^3 = 8 => x^2 - 3x - 8 = 0. Solving gives x = 6.
Correct Answer: B — 6
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Q. If log_2(x) + log_2(x-1) = 3, what is the value of x?
Solution
log_2(x(x-1)) = 3 => x(x-1) = 2^3 = 8 => x^2 - x - 8 = 0. Solving gives x = 5.
Correct Answer: B — 5
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Q. If log_2(x) = 5, what is the value of x?
Solution
log_2(x) = 5 implies x = 2^5 = 32.
Correct Answer: C — 64
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Q. If log_3(9) + log_3(27) = x, what is the value of x?
Solution
log_3(9) = 2 and log_3(27) = 3, thus x = 2 + 3 = 5.
Correct Answer: C — 4
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Q. If log_3(9) = x, what is the value of x?
Solution
log_3(9) = log_3(3^2) = 2.
Correct Answer: B — 2
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Q. If log_3(x + 1) = 2, what is the value of x?
Solution
log_3(x + 1) = 2 implies x + 1 = 3^2 = 9 => x = 8.
Correct Answer: B — 8
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Q. If log_3(x) + log_3(4) = 2, find x.
Solution
log_3(4x) = 2 => 4x = 3^2 = 9 => x = 9/4 = 2.25.
Correct Answer: C — 9
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Q. If log_3(x) = 2, what is the value of x?
Solution
log_3(x) = 2 implies x = 3^2 = 9.
Correct Answer: B — 9
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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
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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?
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A.
x + 1
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B.
2x
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C.
3x
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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
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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(2) = x and log_a(3) = y, then log_a(6) is equal to?
-
A.
x + y
-
B.
xy
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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(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?
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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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