MCQ: Logarithms - 2 - SSC CGL MCQ

# MCQ: Logarithms - 2 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Logarithms - 2

MCQ: Logarithms - 2 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Logarithms - 2 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Logarithms - 2 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Logarithms - 2 below.
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MCQ: Logarithms - 2 - Question 1

### If log 2 = 0.3010, then the number of digits in 264 is ?

Detailed Solution for MCQ: Logarithms - 2 - Question 1

Required answer = [64 log10 2] + 1
= [ 64 x 0.3010 ] + 1
= 19.264 + 1
= 19 + 1
= 20

MCQ: Logarithms - 2 - Question 2

### The value of log23 x log32 x log34 x log43 is ?

Detailed Solution for MCQ: Logarithms - 2 - Question 2

Given Exp.= log23 x log 32 x log34 x log43
= (log3 / log2) x ( log2 / log3) x (log4 / log3) x (log3 / log4) = 1

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MCQ: Logarithms - 2 - Question 3

### The value of log 9/8 - log 27/32 + log3/4 is ?

Detailed Solution for MCQ: Logarithms - 2 - Question 3

Given Exp. = log [{(9/8) / (27/32)} x 3/4)]
= log [(9/8) x (3/4) x (32/27)]
= log 1
= 0

MCQ: Logarithms - 2 - Question 4

The value of  is ?

Detailed Solution for MCQ: Logarithms - 2 - Question 4

∵ loga x = ( logabx) / (logaba)
∴ The given expression = [[(logabx) / (logaba)] / [( logabx )] - ( logab)
= (1/logaba) - logab = logaab - logab = loga(ab/b)
= logaa = 1

MCQ: Logarithms - 2 - Question 5

Given that log10 2 = 0.3010, then log2 10 is equal to ?

Detailed Solution for MCQ: Logarithms - 2 - Question 5

log2 10 = log 10 / log 2
= 1 / log 2
= 1.0000 / 0.3010
= 1000 / 301

MCQ: Logarithms - 2 - Question 6

The simplified form of log(75/16) -2 log(5/9) +log(32/343) is ?

Detailed Solution for MCQ: Logarithms - 2 - Question 6

= log75/16 - 2 log5/9 + log32/343
= log [(25 x 3) / (4 x 4)] - log (25/81) + log [(16 x 2) / (81 x 3)]
= log(25 x 3) - log ( 4 x 4 ) - log(25) + log81 + log(16 x 2) -log (81 x 3)
= log 25 + log 3 - log 16 - log 25 + log 81 + log 16 + log 2 - log 81 - log 3
= log 2

MCQ: Logarithms - 2 - Question 7

If log102 =0.3010 and log107 = 0.8451, then the value of log10 2.8 is ?

Detailed Solution for MCQ: Logarithms - 2 - Question 7

log102.8 = log10(28/10)
= log 28 - log 10
= log (7 x 4 ) - log 10
= log 7 + 2 log 2 - log 10
= 0.8451 + 2 x 0.3010 - 1
= 0.8451 + 0.6020 - 1
= 0.4471

MCQ: Logarithms - 2 - Question 8

Find the value of log (a2 / bc) + log (b2 / ac) + log (c2 / ab) ?

Detailed Solution for MCQ: Logarithms - 2 - Question 8

Given Exp. = log (a2 / bc) + log (b2 / ac) + log (c2 / ab)
= log [(a2 x b2 x c2) / (a2 x b2 x c2)]
= log 1
= 0

MCQ: Logarithms - 2 - Question 9

If log 2 = 0.3010 then log 5 equals to ?

Detailed Solution for MCQ: Logarithms - 2 - Question 9

log 5 = log 10 /2 = log 10 - log 2
= 1 - 0.3010 = 0.6990

MCQ: Logarithms - 2 - Question 10

If log10 2 = 0.301, then the value of log10(50) is ?

Detailed Solution for MCQ: Logarithms - 2 - Question 10

log1050 = log10[(50 x 2) / 2]
= log 100 - log 2
= log10102 - log 2
= 2 - 0.301
= 1.699

MCQ: Logarithms - 2 - Question 11

Find the value of log 8 + log 1/8 ?

Detailed Solution for MCQ: Logarithms - 2 - Question 11

Given expression = log 8 + log (1/8)
= log 8 x (1/8)
= log 1
= 0

MCQ: Logarithms - 2 - Question 12

Find the value of log x + log (1/x) ?

Detailed Solution for MCQ: Logarithms - 2 - Question 12

Given expression = log x + log1/x
= log x + log 1 - log x
= log 1
= 0

MCQ: Logarithms - 2 - Question 13

If 2 log4x = 1 + log4 (x-1), find the value of x. ?

Detailed Solution for MCQ: Logarithms - 2 - Question 13

∵ 2log4x = 1 + log4(x-1)
⇒ log4x2 = log44 + log4(x-1)
⇒ x2 = 4(x-1)
⇒ x2 - 4x + 4 = 0
⇒ (x-2)2 = 0
∴ x = 2

MCQ: Logarithms - 2 - Question 14

The equation logax + loga (1 + x) = 0 can be written as ?

Detailed Solution for MCQ: Logarithms - 2 - Question 14

logax + loga(1+x) = 0
⇒ logax (x+1) = loga1 (since log 1 = 0)
⇒ x(x +1) = 1
∴ x2 + x - 1 = 0

MCQ: Logarithms - 2 - Question 15

If log 90 = 1.9542 then log 3 equals to ?

Detailed Solution for MCQ: Logarithms - 2 - Question 15

Given log90 = 1.9542
⇒ log(32 x 10) = 1.9542
⇒ 2log 3 + log 10 = 1.9542
∴ log 3 = 0.9542 / 2 = 0.4771

## Quantitative Aptitude for SSC CGL

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests