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Mathematics

Logarithm MCQs

Practice Logarithm MCQs for competitive exams.

Logarithm MCQs

Practice questions from this topic.

If $${log _{10}}a = p,$$ $${log _{10}}b = q,$$ then what is $${log _{10}}left( {{a^p}{b^q}} right)$$ equal to?

  1. A. p 2 + q 2
  2. B. p 2 - q 2
  3. C. p 2 q 2
  4. D. $$frac{{{p^2}}}{{{q^2}}}$$
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If $$log 3log left( {{3^x} - 2} right),$$ and $$log left( {{3^x} + 4} right)$$ are in arithmetic progression, then x is equal to

  1. A. $$frac{8}{3}$$
  2. B. $$log {3^8}$$
  3. C. $$log {2^3}$$
  4. D. 8
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The number of digits in $${{text{4}}^9} times {{text{5}}^{17}}{text{,}}$$ when expressed in usual form, is -

  1. A. 16
  2. B. 17
  3. C. 18
  4. D. 19
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If $$log 2 = 0.30103,$$ the number of digits in $${4^{50}}$$ is -

  1. A. 30
  2. B. 31
  3. C. 100
  4. D. 200
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If the logarithm of a number is - 3.153, what are characteristic and mantissa?

  1. A. characteristic = -4, mantissa = 0.847
  2. B. characteristic = -3, mantissa = -0.153
  3. C. characteristic = 4, mantissa = -0.847
  4. D. characteristic = 3, mantissa = -0.153
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If $$log 2 = 0.3010,$$ and $$log 3 = 0.4771,,$$ the value of $${log _5}512$$ = ?

  1. A. 2.870
  2. B. 2.967
  3. C. 3.876
  4. D. 3.912
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If $${text{a}} = {text{lo}}{{text{g}}_{text{8}}},{text{225}}$$ and $${text{b = lo}}{{text{g}}_{text{2}}},{text{15}},$$ then a in terms of b is -

  1. A. $$frac{b}{2}$$
  2. B. $$frac{{2b}}{3}$$
  3. C. b
  4. D. $$frac{{3b}}{2}$$
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If $${log _7}{log _5}left( {sqrt {x + 5} + sqrt x } right)$$ $$ = 0,$$ what is the value of x ?

  1. A. 2
  2. B. 3
  3. C. 4
  4. D. 5
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If $${log _3}x + {log _{9}}{x^2} + {log _{27}}{x^3}$$ $$ = 9,$$ then x equals to -

  1. A. 3
  2. B. 9
  3. C. 27
  4. D. None of these
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If $$a = {b^2} = {c^3} = {d^4},$$ then the value of $${log _a}left( {abcd} right)$$ would be -

  1. A. $${log _a}1 + {log _a}2 + {log _a}3 + {log _a}4$$
  2. B. $${log _a}24$$
  3. C. $${text{1 + }}frac{1}{2} + frac{1}{3} + frac{1}{4}$$
  4. D. $${text{1 + }}frac{1}{{2!}} + frac{1}{{3!}} + frac{1}{{4!}}$$
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If $$log x - 5log 3 = - 2,$$ then x equals -

  1. A. 0.8
  2. B. 0.81
  3. C. 1.25
  4. D. 2.43
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$${frac{1}{{left( {{{log }_a}bc} right) + 1}} + }$$ $${frac{1}{{left( {{{log }_b}ca} right) + 1}} + }$$ $${frac{1}{{left( {{{log }_c}ab} right) + 1}}}$$ is equal to -

  1. A. 1
  2. B. $$frac{3}{2}$$
  3. C. 2
  4. D. 3
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