MCQ: Logarithms - 3 - SSC CGL MCQ

# MCQ: Logarithms - 3 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Logarithms - 3

MCQ: Logarithms - 3 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Logarithms - 3 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Logarithms - 3 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Logarithms - 3 below.
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MCQ: Logarithms - 3 - Question 1

### If log 3 = 0.477 and (1000)x = 3, then x equals to ?

Detailed Solution for MCQ: Logarithms - 3 - Question 1

∵ (1000)x = 3
⇒ xlog 103 = log 3
⇒ 3x = log 3
∴ x = log 3 / 3 = 0.477 / 3 = 0.159

MCQ: Logarithms - 3 - Question 2

### If log8 x + log4 x + log2x =11, then the value of x is ?

Detailed Solution for MCQ: Logarithms - 3 - Question 2

∵ log23 x1 +log22 x1 + log2x = 11
⇒ 1/3log2x + 1/2log2x + log2x = 11
⇒ (1/3 + 1/2 +1)log2x = 11
⇒ 11/6log2x = 11
⇒ log2x = 11 x 6 / 11 =6
∴ x = 26 = 64

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MCQ: Logarithms - 3 - Question 3

### Find the value of log0.125 64 ?

Detailed Solution for MCQ: Logarithms - 3 - Question 3

Exp. = log0.12564 = log2-3 26
={6 / (-3)} log22
= -2

MCQ: Logarithms - 3 - Question 4

If 55-x = 2x-5, find the value of x. ?

Detailed Solution for MCQ: Logarithms - 3 - Question 4

∵ 55-x = 2x-5
⇒ 55-x = 2-(5-x)
⇒ (5-x)log 5 = -(5-x)log 2
⇒ (5-x)log 5 + (5-x)log 2 = 0
⇒ (5-x){log 5 + log 2 } = 0
⇒ (5-x){log10/2 + log 2 } = 0
⇒ (5-x){log10 - log 2 + log 2} = 0
⇒ 5-x = 0
∴ x = 5

MCQ: Logarithms - 3 - Question 5

If 100.3010 = 2, then find the value of log0.125 125. ?

Detailed Solution for MCQ: Logarithms - 3 - Question 5

= log0.125125 = log2-3 53 = - 3/3log25 = -log25
∵ 100.3010 = 2
⇒ log102 = 0.3010
∵ log105 = log1010/2 = log1010-log102
= 1-0.3010 = 0.6990
∴ -log25 = - log105 / log102
= - 0.6990 / 0.3010 = - 699/301

MCQ: Logarithms - 3 - Question 6

Find the value of log3228 + log24337 - log361296 ?

Detailed Solution for MCQ: Logarithms - 3 - Question 6

=log3228 + log24337 - log361296
= log25 28 + log35 37 - log36 362
= (8/5)log22 + (7/5)log33 - 2log3636
= 8/5 + 7/5 - 2 = 1

MCQ: Logarithms - 3 - Question 7

Find the value of log9 81 - log4 32 ?

Detailed Solution for MCQ: Logarithms - 3 - Question 7

log9 81 - log4 32 = log32 34 - log22 25
= 4/2 - 5/2 = -1/2

MCQ: Logarithms - 3 - Question 8

log10x + log10y = z, then x is equal to ?

Detailed Solution for MCQ: Logarithms - 3 - Question 8

log10xy = z
⇒ xy = 10z
⇒ x = 10z/y

MCQ: Logarithms - 3 - Question 9

Find the value of log49 16807 - log9 27 ?

Detailed Solution for MCQ: Logarithms - 3 - Question 9

= log4916807 - log927
= log72 75 - log32 33
=(5/2)log77 - (3/2)log33
=5/2 - 3/2
= 1

MCQ: Logarithms - 3 - Question 10

log1010 + log10100 + log101000 + log1010000 + log10100000 is equal to ?

Detailed Solution for MCQ: Logarithms - 3 - Question 10

= log1010 + log10100 + log101000 + log1010000 + log10100000
= 1 + 2 + 3 + 4 + 5
= 15

MCQ: Logarithms - 3 - Question 11

log-1/3 81 is equal to ?

Detailed Solution for MCQ: Logarithms - 3 - Question 11

Let log-1/381 = x
⇒ 81 = (-1/3)x
⇒ 34 = (-1/3)x = 3-x
∴ x = -4

MCQ: Logarithms - 3 - Question 12

The value of 25 log5 4 is ?

Detailed Solution for MCQ: Logarithms - 3 - Question 12

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

MCQ: Logarithms - 3 - Question 13

The value of log10 (0.00001) is ?

Detailed Solution for MCQ: Logarithms - 3 - Question 13

= log10 10-5 = -5

MCQ: Logarithms - 3 - Question 14

If log10 {log10[log10(log10N)]} = 0, then the value of N is ?

Detailed Solution for MCQ: Logarithms - 3 - Question 14

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

MCQ: Logarithms - 3 - Question 15

The value of log10 0.000001 is ?

Detailed Solution for MCQ: Logarithms - 3 - Question 15

= log10 10-6 = -6

## Quantitative Aptitude for SSC CGL

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests