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RRB NTPC/ASM/CA/TA Exam  >  RRB NTPC/ASM/CA/TA Test  >  Mathematics for RRB NTPC / ASM  >  MCQ: Logarithms - 3 - RRB NTPC/ASM/CA/TA MCQ

Logarithms - 3 - Free MCQ Practice Test with solutions, RRB NTPC/ASM/CA/TA


MCQ Practice Test & Solutions: MCQ: Logarithms - 3 (15 Questions)

You can prepare effectively for RRB NTPC/ASM/CA/TA Mathematics for RRB NTPC / ASM with this dedicated MCQ Practice Test (available with solutions) on the important topic of "MCQ: Logarithms - 3". These 15 questions have been designed by the experts with the latest curriculum of RRB NTPC/ASM/CA/TA 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 15 minutes
  • - Number of Questions: 15

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MCQ: Logarithms - 3 - Question 1
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If log 3 = 0.477 and (1000)x = 3, then x equals to ?

Detailed Solution: 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
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If log8 x + log4 x + log2x =11, then the value of x is ?

Detailed Solution: 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
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Find the value of log0.125 64 ?

Detailed Solution: Question 3

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

MCQ: Logarithms - 3 - Question 4
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If 55-x = 2x-5, find the value of x. ?

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

Detailed Solution: 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
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Find the value of log3228 + log24337 - log361296 ?

Detailed Solution: 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
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Find the value of log9 81 - log4 32 ?

Detailed Solution: Question 7

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

MCQ: Logarithms - 3 - Question 8
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log10x + log10y = z, then x is equal to ?

Detailed Solution: Question 8

log10xy = z
⇒ xy = 10z
⇒ x = 10z/y 

MCQ: Logarithms - 3 - Question 9
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Find the value of log49 16807 - log9 27 ?

Detailed Solution: Question 9

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

MCQ: Logarithms - 3 - Question 10
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log1010 + log10100 + log101000 + log1010000 + log10100000 is equal to ?

Detailed Solution: Question 10

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

MCQ: Logarithms - 3 - Question 11
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log-1/3 81 is equal to ?

Detailed Solution: Question 11

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

MCQ: Logarithms - 3 - Question 12
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The value of 25 log5 4 is ?

Detailed Solution: Question 12

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

MCQ: Logarithms - 3 - Question 13
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The value of log10 (0.00001) is ?

Detailed Solution: Question 13

= log10 10-5 = -5

MCQ: Logarithms - 3 - Question 14
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If log10 {log10[log10(log10N)]} = 0, then the value of N is ?

Detailed Solution: Question 14

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

MCQ: Logarithms - 3 - Question 15
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The value of log10 0.000001 is ?

Detailed Solution: Question 15

= log10 10-6 = -6

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About this RRB NTPC/ASM/CA/TA Practice Test

This test contains 15 MCQs on MCQ: Logarithms - 3 with detailed solutions for each question. It is part of the Mathematics for RRB NTPC / ASM course on EduRev, designed to align with the current RRB NTPC/ASM/CA/TA syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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