If p x = q, then? logp x = q logx q = P logp q = x logq P = x ? px = q ? logppx

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Home ‣ Aptitude ‣ Logarithm Comments

Question
If p ^x = q, then?
Options
A. logp x = q
B. logx q = P
C. logp q = x
D. logq P = x

Correct Answer

logp q = x

Explanation

? p^x = q
? log_pp^x = log_pq
? xlog_pp = log_pq
? x = log_pq (?log_pp = 1)

Logarithm problems

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1.
If log ₁₀ x = 7, then value of x is?
Options
A. 1010
B. 107
C. 710
D. None of these

Discuss

Correct Answer: 107

Explanation:

log₁₀x = 7
? x = 10⁷

2.
If log _a 3 = 1/3, then value of a is?
Options
A. 27
B. 81
C. 72
D. None of these

Discuss

Correct Answer: 27

Explanation:

? log_a3 = 1/3
? 3 = (a)^1/3
? a = 27

3.
The value of log ₂ (1/64) is?
Options
A. 6
B. - 6
C. 7
D. None of these

Discuss

Correct Answer: - 6

Explanation:

log₂(1/64) = log₂1 - log₂ 2⁶
= 0 - 6 = -6

4.
log _x (16/25) = -1/2, then x is?
Options
A. 625 / 256
B. 256 / 625
C. 526 / 265
D. None of these

Discuss

Correct Answer: 625 / 256

Explanation:

? log_x(16/25) = -1/2
? 16/25 = (x)^-1/2 = 1/x^1/2
? x = 625/256

5.
If log ₁₀₀₀₀x = -1/4, then x is?
Options
A. 1 / 100
B. 1 / 10
C. 1 / 20
D. None of these

Discuss

Correct Answer: 1 / 10

Explanation:

? log₁₀⁴x = -1/4
? x = (10⁴)^-1/4
= 1/10

6.
Given that log ₁₀ 2 = 0.3010 the value of log ₁₀ 5 is?
Options
A. 0.3241
B. 0.6911
C. 0.6990
D. 0.7525

Discuss

Correct Answer: 0.6990

Explanation:

log₁₀5 = log₁₀(10/2)
= log₁₀10 - log₁₀2
= 1-0.3010
= 0.6990

7.
If log ₁₀ (10x) = 2.7532, then log ₁₀ (10000x) is?
Options
A. 4.7532
B. 5.7532
C. 3 x 2.7532
D. None of these

Discuss

Correct Answer: 5.7532

Explanation:

log₁₀(10³.10x) = log₁₀ 10³ + log₁₀(10x)
= 3 + 2.7532
= 5.7532

8.
If log 125 / log 5 = x, then x is equal to?
Options
A. 2
B. 3
C. 4
D. 1 / 2

Discuss

Correct Answer: 3

Explanation:

If log 125 / log 5 = x
then x = 3log5 / log5= 3

9.
(log ₅ 3 ) x (log ₃ 625) is equal to?
Options
A. 1
B. 2
C. 3
D. 4

Discuss

Correct Answer: 4

Explanation:

(log₅3) x log₃ 5⁴ = [log3 / log5] x 4 x [log5 / log3]
= 4

10.
log ₉ 27 - log ₂₇ 9 is equal to?
Options
A. 6 / 5
B. 5 / 6
C. 3
D. 32

Discuss

Correct Answer: 5 / 6

Explanation:

Given Exp. = log₉27 - log₂₇9
= log27 / log9 - log9 / log27
= 3log3 / 2log3 - 2log3 / 3log3
= 3/2 - 2/3 = 5/6

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If p ^x = q, then?