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Quantitative Aptitude

LOGARITHM MCQs

Logarithms

Total Questions : 289 | Page 7 of 29 pages
Question 61. If $${\log _{10}}2 = a$$  and $${\log _{10}}3 = b,$$   then $${\log _5}12$$ = ?
  1.    $$\frac{{a + b}}{{1 + a}}$$
  2.    $$\frac{{2a + b}}{{1 + a}}$$
  3.    $$\frac{{a + 2b}}{{1 + a}}$$
  4.    $$\frac{{2a + b}}{{1 - a}}$$
 Discuss Question
Answer: Option D. -> $$\frac{{2a + b}}{{1 - a}}$$
Question 62. If $${\log _a}\left( {ab} \right) = x{\text{,}}\,$$   then $${\log _b}\left( {ab} \right)$$   is -
  1.    $$\frac{1}{x}$$
  2.    $$\frac{x}{{x + 1}}$$
  3.    $$\frac{x}{{1 - x}}$$
  4.    $$\frac{x}{{x - 1}}$$
 Discuss Question
Answer: Option D. -> $$\frac{x}{{x - 1}}$$
Question 63. If $${\log _{10}}125 + {\log _{10}}8 = x,$$     then x is equal to -
  1.    $$\frac{1}{3}$$
  2.    0.064
  3.    -3
  4.    3
 Discuss Question
Answer: Option D. -> 3
Question 64. If $${\log _5}\left( {{x^2} + x} \right) - $$   $${\log _5}\left( {x + 1} \right)$$   = 2, then the value of x is -
  1.    5
  2.    10
  3.    25
  4.    32
 Discuss Question
Answer: Option C. -> 25
Question 65. $$\frac{1}{2}\left( {\log x + \log y} \right)$$    will equal to $$\log \left( {\frac{{x + y}}{2}} \right)$$   if -
  1.    y = 0
  2.    x = $$\sqrt {\text{y}} $$
  3.    x = y
  4.    x = $$\frac{{\text{y}}}{2}$$
 Discuss Question
Answer: Option C. -> x = y
Question 66. $${\log \left( {\frac{{{a^2}}}{{bc}}} \right) + }$$   $${\log \left( {\frac{{{b^2}}}{{ac}}} \right) + }$$   $${\log \left( {\frac{{{c^2}}}{{ab}}} \right)}$$   is equal to -
  1.    0
  2.    1
  3.    2
  4.    abc
 Discuss Question
Answer: Option A. -> 0
Question 67. If $$\log \frac{a}{b} + \log \frac{b}{a} = $$   $$\,\log \left( {a + b} \right),$$   then -
  1.    a + b = 1
  2.    a - b = 1
  3.    a = b
  4.    a2 - b2 = 1
 Discuss Question
Answer: Option A. -> a + b = 1
Question 68. $$\frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}}$$     is equal to -
  1.    a + b + c
  2.    abc
  3.    0
  4.    1
 Discuss Question
Answer: Option D. -> 1
Question 69. $${\frac{1}{{\left( {{{\log }_a}bc} \right) + 1}} + }$$   $${\frac{1}{{\left( {{{\log }_b}ca} \right) + 1}} + }$$   $${\frac{1}{{\left( {{{\log }_c}ab} \right) + 1}}}$$   is equal to -
  1.    1
  2.    $$\frac{3}{2}$$
  3.    2
  4.    3
 Discuss Question
Answer: Option A. -> 1
Question 70. If $${\log _{10}}7 = a,$$   then $${\log _{10}}\left( {\frac{1}{{70}}} \right)$$   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)

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