Logarithm MCQ

Test your knowledge with important Logarithm MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Logarithm MCQs at Bissoy

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

  p² + q²

  খ

  p² - q²

  গ

  p²q²

  ঘ

  $$\frac{{{p^2}}}{{{q^2}}}$$
• If $$\log 3\log \left( {{3^x} - 2} \right)\,$$   and $$\log \left( {{3^x} + 4} \right)$$   are in arithmetic progression, then x is equal to
  ক

  $$\frac{8}{3}$$

  খ

  $$\log {3^8}$$

  গ

  $$\log {2^3}$$

  ঘ

  8
• The number of digits in $${{\text{4}}^9} \times {{\text{5}}^{17}}{\text{,}}$$   when expressed in usual form, is -
  ক

  16

  খ

  17

  গ

  18

  ঘ

  19
• If $$\log 2 = 0.30103,$$    the number of digits in $${4^{50}}$$ is -
  ক

  30

  খ

  31

  গ

  100

  ঘ

  200
• If the logarithm of a number is - 3.153, what are characteristic and mantissa?
  ক

  characteristic = -4, mantissa = 0.847

  খ

  characteristic = -3, mantissa = -0.153

  গ

  characteristic = 4, mantissa = -0.847

  ঘ

  characteristic = 3, mantissa = -0.153
• If $$\log 2 = 0.3010\,$$   and $$\log 3 = 0.4771,\,$$   the value of $${\log _5}512$$   = ?
  ক

  2.870

  খ

  2.967

  গ

  3.876

  ঘ

  3.912
• 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 -
  ক

  $$\frac{b}{2}$$

  খ

  $$\frac{{2b}}{3}$$

  গ

  b

  ঘ

  $$\frac{{3b}}{2}$$
• If $${\log _7}{\log _5}\left( {\sqrt {x + 5} + \sqrt x } \right)$$     $$ = 0,$$  what is the value of x ?
  ক

  2

  খ

  3

  গ

  4

  ঘ

  5
• If $${\log _3}x + {\log _{9}}{x^2} + {\log _{27}}{x^3}$$     $$ = 9,$$  then x equals to -
  ক

  3

  খ

  9

  গ

  27

  ঘ

  None of these
• If $$a = {b^2} = {c^3} = {d^4},$$    then the value of $${\log _a}\left( {abcd} \right)$$   would be -
  ক

  $${\log _a}1 + {\log _a}2 + {\log _a}3 + {\log _a}4$$      

  খ

  $${\log _a}24$$

  গ

  $${\text{1 + }}\frac{1}{2} + \frac{1}{3} + \frac{1}{4}$$  

  ঘ

  $${\text{1 + }}\frac{1}{{2!}} + \frac{1}{{3!}} + \frac{1}{{4!}}$$  
• If $$\log x - 5\log 3 = - 2,$$     then x equals -
  ক

  0.8

  খ

  0.81

  গ

  1.25

  ঘ

  2.43
• If $${\log _{10}}7 = a,$$   then $${\log _{10}}\left( {\frac{1}{{70}}} \right)$$   is equal to -
  ক

  -(1 + a)

  খ

  (1 + a)^-1

  গ

  $$\frac{a}{{10}}$$

  ঘ

  $$\frac{1}{{10a}}$$
• $${\frac{1}{{\left( {{{\log }_a}bc} \right) + 1}} + }$$   $${\frac{1}{{\left( {{{\log }_b}ca} \right) + 1}} + }$$   $${\frac{1}{{\left( {{{\log }_c}ab} \right) + 1}}}$$   is equal to -
  ক

  1

  খ

  $$\frac{3}{2}$$

  গ

  2

  ঘ

  3
• $$\frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}}$$     is equal to -
  ক

  a + b + c

  খ

  abc

  গ

  0

  ঘ

  1
• $${\log \left( {\frac{{{a^2}}}{{bc}}} \right) + }$$   $${\log \left( {\frac{{{b^2}}}{{ac}}} \right) + }$$   $${\log \left( {\frac{{{c^2}}}{{ab}}} \right)}$$   is equal to -
  ক

  0

  খ

  1

  গ

  2

  ঘ

  abc
• If $$\log \frac{a}{b} + \log \frac{b}{a} = $$   $$\,\log \left( {a + b} \right),$$   then -
  ক

  a + b = 1

  খ

  a - b = 1

  গ

  a = b

  ঘ

  a² - b² = 1
• $$\frac{1}{2}\left( {\log x + \log y} \right)$$    will equal to $$\log \left( {\frac{{x + y}}{2}} \right)$$   if -
  ক

  y = 0

  খ

  x = $$\sqrt {\text{y}} $$

  গ

  x = y

  ঘ

  x = $$\frac{{\text{y}}}{2}$$
• If $${\log _5}\left( {{x^2} + x} \right) - $$   $${\log _5}\left( {x + 1} \right)$$   = 2, then the value of x is -
  ক

  5

  খ

  10

  গ

  25

  ঘ

  32
• If $${\log _{10}}125 + {\log _{10}}8 = x,$$     then x is equal to -
  ক

  $$\frac{1}{3}$$

  খ

  0.064

  গ

  -3

  ঘ

  3
• If $${\log _{10}}2 = a$$  and $${\log _{10}}3 = b,$$   then $${\log _5}12$$ = ?
  ক

  $$\frac{{a + b}}{{1 + a}}$$

  খ

  $$\frac{{2a + b}}{{1 + a}}$$

  গ

  $$\frac{{a + 2b}}{{1 + a}}$$

  ঘ

  $$\frac{{2a + b}}{{1 - a}}$$
• If $${\log _a}\left( {ab} \right) = x{\text{,}}\,$$   then $${\log _b}\left( {ab} \right)$$   is -
  ক

  $$\frac{1}{x}$$

  খ

  $$\frac{x}{{x + 1}}$$

  গ

  $$\frac{x}{{1 - x}}$$

  ঘ

  $$\frac{x}{{x - 1}}$$
• $$2{\log _{10}}^5 + $$  $${\log _{10}}8 \,- $$  $$\frac{1}{2}{\log _{10}}4$$   = ?
  ক

  2

  খ

  4

  গ

  $${\text{2 - 2 lo}}{{\text{g}}_{10}}^2$$

  ঘ

  $${\text{4 - 4 lo}}{{\text{g}}_{10}}^2$$
• The value of $$\frac{{6{\text{ }}{{\log }_{10}}1000}}{{3{\text{ }}{{\log }_{10}}100}}$$   is equal to -
  ক

  0

  খ

  1

  গ

  2

  ঘ

  3
• $$\frac{{\log \sqrt 8 }}{{\log 8}}\,\,{\text{is equal to = ?}}$$
  ক

  $$\frac{1}{{\sqrt 8 }}$$

  খ

  $$\frac{1}{4}$$

  গ

  $$\frac{1}{2}$$

  ঘ

  $$\frac{1}{8}$$
• If $${\log _{10000}}x = - \frac{1}{4}{\text{,}}$$    then the value of x is = ?
  ক

  $$\frac{1}{{10}}$$

  খ

  $$\frac{1}{{100}}$$

  গ

  $$\frac{1}{{1000}}$$

  ঘ

  $$\frac{1}{{10000}}$$
• If $${\text{lo}}{{\text{g}}_8}{\text{p}} = 25$$   and $${\text{lo}}{{\text{g}}_2}{\text{q}} = 5,$$   then -
  ক

  p = q¹⁵

  খ

  p² = q³

  গ

  p = q⁵

  ঘ

  p³ = q
• The value of $${\text{lo}}{{\text{g}}_{10}}\left( {0.0001} \right)$$   is = ?
  ক

  $$\frac{1}{4}$$

  খ

  $$ - \frac{1}{4}$$

  গ

  $$ - 4$$

  ঘ

  $$4$$
• Determine the value of $${\text{lo}}{{\text{g}}_{3\sqrt 2 }}\left( {\frac{1}{{18}}} \right)$$   is = ?
  ক

  2

  খ

  -2

  গ

  $$\sqrt 2 $$

  ঘ

  $$\sqrt 3 $$
• The value of $${\log _5}\frac{{\left( {125} \right)\left( {625} \right)}}{{25}}$$    is equal to -
  ক

  725

  খ

  5

  গ

  3125

  ঘ

  6
• The value of log₂ 16 is:
  ক

  $$\frac{1}{8}$$

  খ

  4

  গ

  8

  ঘ

  16