If log 10000x = -1/4, then x is? 1 / 100 1 / 10 1 / 20 None of these ? log104x =

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Home ‣ Aptitude ‣ Logarithm Comments

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

Correct Answer

1 / 10

Explanation

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

Logarithm problems

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1.
The value of log ₆ log ₅ 15625 is?
Options
A. 1
B. 2
C. 3
D. None of these

Discuss

Correct Answer: 1

Explanation:

log₆ log₅15625 = log₆ log₅(5)⁶
= log₆6(log₅5) = 1

2.
The value of log ₁₀ (0.00001) is?
Options
A. - 5
B. - 6
C. - 7
D. None of these

Discuss

Correct Answer: - 5

Explanation:

Exp. = log₁₀ 10^-5 = -5

3.
The value of log ₁₀ 0.000001 is?
Options
A. 6
B. - 6
C. 5
D. - 5

Discuss

Correct Answer: - 6

Explanation:

Exp. = log₁₀ 10^-6 = -6

4.
The value of 25 log ₅ 4 is?
Options
A. 16
B. 5
C. 25
D. None of these

Discuss

Correct Answer: 16

Explanation:

Exp. = 25 log₅4 = 5² log₅4
= 5 log₅ 4²
= 16

5.
If log ₁₀ {log ₁₀[log ₁₀(log ₁₀N )]} = 0, then the value of N is?
Options
A. 1010
B. 101010
C. 10-10
D. 10102

Discuss

Correct Answer: 101010

Explanation:

If log₁₀{log₁₀[log₁₀(log₁₀N)]} = 0
? log₁₀{log₁₀(log₁₀N)} = 1
? log₁₀(log₁₀N) = 10
? log₁₀^N = 10¹⁰
? N = 10¹⁰¹⁰

6.
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

7.
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

8.
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

9.
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

10.
If p ^x = q, then?
Options
A. logp x = q
B. logx q = P
C. logp q = x
D. logq P = x

Discuss

Correct Answer: logp q = x

Explanation:

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

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If log 10000x = -1/4, then x is?

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If log ₁₀₀₀₀x = -1/4, then x is?