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Quantitative Aptitude

LOGARITHM MCQs

Logarithms

Total Questions : 289 | Page 3 of 29 pages
Question 21.

Which of the following statements is not correct?

  1.    log10 10 = 1
  2.    log (2 + 3) = log (2 x 3)
  3.    log10 1 = 0
  4.    log (1 + 2 + 3) = log 1 + log 2 + log 3
 Discuss Question
Answer: Option B. -> log (2 + 3) = log (2 x 3)

(a) Since loga a = 1, so log10 10 = 1.


(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3


     So,  log (2 + 3)  Which Of The Following Statements Is Not Correct? log (2 x 3)


(c) Since loga 1 = 0, so log10 1 = 0.


(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.


So, (b) is incorrect.

Question 22.

If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:


 

  1.    2.870
  2.    2.967
  3.    3.876
  4.    3.912
 Discuss Question
Answer: Option C. -> 3.876

log5 512  =  \(\frac{\log512}{\log5}\)


\(\frac{\log2^{9}}{\log(\frac{10}{2})}\)


= \(\frac{9\log2}{\log10-\log2}\)


\(\frac{(9\times0.3010)}{1-0.3010}\)


= \(\frac{2.709}{0.699}\)


= \(\frac{2709}{699}\)


=3.876

Question 23.

   \(\frac{\log8}{\log8}\)   is equal to:

  1.    \(\frac{1}{8}\)
  2.    \(\frac{1}{4}\)
  3.    \(\frac{1}{2}\)
  4.    \(\frac{1}{8}\)
 Discuss Question
Answer: Option C. -> \(\frac{1}{2}\)

\(\frac{\log8}{\log8} = \frac{\log8^{\frac{1}{2}}}{\log8}=\frac{\frac{1}{2}\log8}{\log8}=\frac{1}{2}\)

Question 24.

If log  \(\frac{a}{b}\) + log  \(\frac{b}{a}\) = log (a + b), then:

  1.    a + b = 1
  2.    a - b = 1
  3.    a = b
  4.    a2 - b2 = 1
 Discuss Question
Answer: Option A. -> a + b = 1

log \(\frac{a}{b}\)   +log  \(\frac{b}{a}\)   = log (a + b)


 log (a + b) = log   \(\log\left(\frac{a}{b}\times\frac{b}{a}\right)\)  = log 1.


o, a + b = 1.

Question 25.

If log10 7 = a, then log10 \(\left(\frac{1}{70}\right)\)   is equal to:

  1.    - (1 + a)
  2.    (1 + a)-1
  3.    \(\frac{a}{10}\)
  4.    \(\frac{1}{10a}\)
 Discuss Question
Answer: Option A. -> - (1 + a)

log10   \(\left(\frac{1}{70}\right)\)   = log10 1 - log10 70


= - log10 (7 x 10)


= - (log10 7 + log10 10)


= - (a + 1).

Question 26.

If log10 2 = 0.3010, then log2 10 is equal to:

  1.    \(\frac{699}{301}\)
  2.    \(\frac{1000}{301}\)
  3.    0.3010
  4.    0.6990
 Discuss Question
Answer: Option B. -> \(\frac{1000}{301}\)

\(\log_{2}10=\frac{1}{\log_{10}2}=\frac{1}{0.310}=\frac{10000}{3010}=\frac{1000}{301}\)

Question 27.

If log10 2 = 0.3010, the value of log10 80 is:

  1.    1.6020
  2.    1.9030
  3.    3.9030
  4.    None of these
 Discuss Question
Answer: Option B. -> 1.9030

log10 80 = log10 (8 x 10)


= log10 8 + log10 10


= log10 (23 ) + 1


= 3 log10 2 + 1


= (3 x 0.3010) + 1


= 1.9030.

Question 28.

If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:

  1.    1
  2.    3
  3.    5
  4.    10
 Discuss Question
Answer: Option B. -> 3

log10 5 + log10 (5x + 1) = log10 (x + 5) + 1


 log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10


 log10 [5 (5x + 1)] = log10 [10(x + 5)]


 5(5x + 1) = 10(x + 5)


 5x + 1 = 2x + 10


 3x = 9


 x = 3.

Question 29.

The value of \(\left(\frac{1}{\log_{3}60}+\frac{1}{\log_{4}60}+\frac{1}{\log_{5}60}\right) is:\)

  1.    0
  2.    1
  3.    5
  4.    60
 Discuss Question
Answer: Option B. -> 1

Given expression= log60 3 + log60 4 + log60 5


= log60 (3 x 4 x 5)


= log60 60


= 1.

Question 30.

If log 2 = 0.30103, the number of digits in 264 is:

  1.    18
  2.    19
  3.    20
  4.    21
 Discuss Question
Answer: Option C. -> 20

log (264)= 64 x log 2


= (64 x 0.30103)


= 19.26592


Its characteristic is 19.


Hence, then number of digits in 264 is 20.

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