8th Class Mathematics Related to Competitive Exam Question Bank

done Logarithms Total Questions - 30

• question_answer1)
  Evaluate: \[{{\log }_{4}}3\times {{\log }_{27}}64\]
  A)
   \[\frac{1}{2}\]                          done clear
  B)
   \[\frac{2}{3}\]              done clear
  C)
   1 done clear
  D)
   \[\frac{1}{3}\] done clear
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• question_answer2)
  Evaluate: \[\text{lo}{{\text{g}}_{16}}64-\text{lo}{{\text{g}}_{64}}16\]
  A)
   6                                 done clear
  B)
   \[\frac{1}{6}\] done clear
  C)
   \[\frac{6}{5}\]                              done clear
  D)
   \[\frac{5}{6}\] done clear
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• question_answer3)
  Find the value of x which satisfies the relation \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{2+lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{(4x+1)=lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{(x+1)+1}\]
  A)
   4                                 done clear
  B)
   -4 done clear
  C)
   1/4                               done clear
  D)
   not defined done clear
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• question_answer4)
  Simplify: \[\left[ \frac{1}{{{\log }_{xy}}(xyz)}+\frac{1}{{{\log }_{yz}}(xyz)}+\frac{1}{{{\log }_{zx}}(xyz)} \right]\]
  A)
   1                                 done clear
  B)
   2 done clear
  C)
   3                                 done clear
  D)
   0 done clear
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• question_answer5)
  The value of log3 81 is equal to:
  A)
   -27                               done clear
  B)
   -4 done clear
  C)
   4                                 done clear
  D)
   27 done clear
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• question_answer6)
  \[\frac{\mathbf{log}\sqrt[\mathbf{3}]{\mathbf{6}}}{\mathbf{log6}}\] is equal to:
  A)
   \[\frac{1}{\sqrt{8}}\]                             done clear
  B)
   \[\frac{1}{4}\]                done clear
  C)
   \[\frac{1}{3}\]           done clear
  D)
   \[\frac{1}{8}\] done clear
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• question_answer7)
  Which of the following statements is correct?
  A)
   \[\text{lo}{{\text{g}}_{10}}10=0\]                    done clear
  B)
   \[\text{log}\left( 2-3 \right)=\text{log}\left( 2\times 3 \right)\] done clear
  C)
   \[\text{lo}{{\text{g}}_{10}}1=1\]                        done clear
  D)
   \[\text{log}\left( \text{1}\times 2\times 3 \right)=\text{log}\,1+\text{log}\,2+\text{log}\,3\] done clear
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• question_answer8)
  If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{2}}}\left[ \mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{2}}}\mathbf{x} \right) \right]\mathbf{=1}\]then x is equal to:
  A)
   0                     done clear
  B)
   12             done clear
  C)
   128                              done clear
  D)
   512 done clear
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• question_answer9)
  log 160 is equal to:
  A)
   \[2\,\text{log}\,2+3\,\text{log}\,3\]          done clear
  B)
   \[~3\,\text{log}\,2+2\,\text{log}\,3\] done clear
  C)
   \[3\,\text{log}2+2\,\text{log}\,3-\text{log}\,5\] done clear
  D)
   \[5\,\text{log}\,2+\text{log}\,5\] done clear
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• question_answer10)
  If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{a}}}\mathbf{(ab)=x,}\] then \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{b}}}\](ab) is:
  A)
   \[\frac{1}{x}\]                          done clear
  B)
   \[\frac{x}{x+1}\] done clear
  C)
   \[\frac{x}{1-x}\]                        done clear
  D)
   \[\frac{x}{x-1}\] done clear
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• question_answer11)
  If \[\mathbf{log2}=\mathbf{x},\,\,\mathbf{log3}=\mathbf{y}\] and \[\mathbf{log7}=\mathbf{z},\]then the value of \[\mathbf{log(8}\mathbf{.}\sqrt[\mathbf{3}]{\mathbf{21}}\mathbf{)}\]is:
  A)
   \[2x+\frac{2}{3}y-\frac{1}{3}z\]           done clear
  B)
   \[2x+\frac{2}{3}y+\frac{1}{3}z\] done clear
  C)
   \[2x-\frac{2}{3}y+\frac{1}{3}z\]           done clear
  D)
   \[3x+\frac{1}{3}y+\frac{1}{3}z\] done clear
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• question_answer12)
  If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{8}}}\mathbf{x+lo}{{\mathbf{g}}_{\mathbf{8}}}\frac{\mathbf{1}}{\mathbf{6}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{3}}\mathbf{,}\] then the value of x is:
  A)
   12     done clear
  B)
   16 done clear
  C)
   18                                done clear
  D)
   24 done clear
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• question_answer13)
  If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{x+2lo}{{\mathbf{g}}_{\mathbf{25}}}\mathbf{x+3lo}{{\mathbf{g}}_{\mathbf{125}}}\mathbf{=9,}\] then x = _______.
  A)
   6                                 done clear
  B)
   36              done clear
  C)
   125   done clear
  D)
   None of these done clear
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• question_answer14)
  If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{5+lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \mathbf{5x+1} \right)\mathbf{=lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \mathbf{x+5} \right)\mathbf{+1,}\]then x is equal to:
  A)
   1                                 done clear
  B)
   3 done clear
  C)
   5                                 done clear
  D)
   10 done clear
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• question_answer15)
  If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\left( {{\mathbf{x}}^{\mathbf{2}}}\mathbf{+x} \right)\mathbf{-lo}{{\mathbf{g}}_{\mathbf{5}}}\left( \mathbf{x+l} \right)\mathbf{=2}\], then the value of x is:
  A)
   5                                 done clear
  B)
   10 done clear
  C)
   25 done clear
  D)
   32 done clear
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• question_answer16)
  The value of \[\left( \frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{60}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{4}}}\mathbf{60}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{60}} \right)\]is:
  A)
   0                                 done clear
  B)
   1  done clear
  C)
   5                                 done clear
  D)
   60 done clear
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• question_answer17)
  The value of \[\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{4} \right)\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{4}}}\mathbf{5} \right)\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{6} \right)\]\[\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{6}}}\mathbf{7} \right)\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{7}}}\mathbf{8} \right)\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{8}}}\mathbf{9} \right)\]is:
  A)
   2                                 done clear
  B)
   7              done clear
  C)
   8 done clear
  D)
   33 done clear
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• question_answer18)
  The value of \[\mathbf{1}{{\mathbf{6}}^{\mathbf{lo}{{\mathbf{g}}_{\mathbf{4}}}}}^{\mathbf{5}}\] is:
  A)
   \[\frac{5}{64}\]                         done clear
  B)
   5               done clear
  C)
   16                                done clear
  D)
   25 done clear
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• question_answer19)
  \[\left[ \frac{1}{\left( {{\log }_{x}}yz \right)+1}+\frac{1}{\left( {{\log }_{y}}zx \right)+1}+\frac{1}{\left( {{\log }_{z}}xz \right)+1} \right]\]is equal to:
  A)
   1   done clear
  B)
   \[\frac{3}{2}\]                done clear
  C)
   2                                 done clear
  D)
   3 done clear
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• question_answer20)
  If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{8=x,}\]then \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \frac{\mathbf{1}}{\mathbf{80}} \right)\]is equal to:
  A)
   \[-\left( 1+x \right)\]  done clear
  B)
   \[{{\left( 1+x \right)}^{-1}}\] done clear
  C)
   \[\frac{a}{10}\]                         done clear
  D)
   \[\frac{1}{10a}\] done clear
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• question_answer21)
  If \[\mathbf{x}={{\mathbf{y}}^{x}},\mathbf{y}={{z}^{y}}\mathbf{and}\,\mathbf{z}={{\mathbf{x}}^{y}},\]then the value of xyz equal to:
  A)
   -1                                done clear
  B)
   0               done clear
  C)
   1    done clear
  D)
   xyz done clear
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• question_answer22)
  \[\frac{\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{6}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{2+1}}\mathbf{=}\]
  A)
   \[lo{{g}_{2}}6\]                       done clear
  B)
   \[lo{{g}_{2}}5\]            done clear
  C)
   \[lo{{g}_{10}}6\] done clear
  D)
   \[lo{{g}_{10}}30\] done clear
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• question_answer23)
  If \[\mathbf{x}=\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}27\]and\[\mathbf{y}=\mathbf{lo}{{\mathbf{g}}_{9}}27\],then \[\frac{\mathbf{1}}{\mathbf{x}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{y}}\mathbf{=}\] _____.
  A)
   \[\frac{1}{3}\]                          done clear
  B)
   \[\frac{1}{9}\]             done clear
  C)
   3                                 done clear
  D)
   1 done clear
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• question_answer24)
  If \[\mathbf{log}\left( \mathbf{0}\mathbf{.37} \right)\mathbf{=}\overline{\mathbf{1}}\mathbf{.756,}\]then the value of \[\mathbf{log37}+\mathbf{log}{{\left( \mathbf{0}.\mathbf{37} \right)}^{\mathbf{3}}}+\mathbf{log}\sqrt{0.\mathbf{37}}\]is:
  A)
   0.902                           done clear
  B)
   \[\overline{2}.146\]              done clear
  C)
   3.444  done clear
  D)
   \[\overline{1}.1\text{ }46\] done clear
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• question_answer25)
  The value of \[\frac{\mathbf{1}}{\mathbf{1+lo}{{\mathbf{g}}_{\mathbf{ab}}}\mathbf{c}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{1+lo}{{\mathbf{g}}_{\mathbf{ac}}}\mathbf{b}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{1+lo}{{\mathbf{g}}_{\mathbf{bc}}}\mathbf{a}}\]equals
  A)
   2   done clear
  B)
   0               done clear
  C)
   1                                 done clear
  D)
   log abc done clear
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• question_answer26)
  If \[{{\mathbf{2}}^{\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{9}}}\mathbf{+2}{{\mathbf{5}}^{\mathbf{lo}{{\mathbf{g}}_{\mathbf{9}}}\mathbf{3}}}\mathbf{=}{{\mathbf{8}}^{\mathbf{lo}{{\mathbf{g}}_{\mathbf{x}}}\mathbf{9}}}\mathbf{,}\] then x = ________.
  A)
   9                     done clear
  B)
   8 done clear
  C)
   3                                 done clear
  D)
   2 done clear
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• question_answer27)
  What is \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \frac{\mathbf{3}}{\mathbf{2}} \right)\mathbf{+lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \frac{\mathbf{4}}{\mathbf{3}} \right)\mathbf{+lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \frac{\mathbf{5}}{\mathbf{4}} \right)\mathbf{+}.....\]up to 10 terms equal to?
  A)
   0                                 done clear
  B)
   \[lo{{g}_{10}}6\] done clear
  C)
   \[lo{{g}_{10}}5\]                      done clear
  D)
   None of these done clear
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• question_answer28)
  What is the value of \[{{\left[ \mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \mathbf{5 lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{100} \right) \right]}^{\mathbf{2}}}_{\mathbf{b}}\]
  A)
   4                     done clear
  B)
   3              done clear
  C)
   2                                 done clear
  D)
   1 done clear
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• question_answer29)
  What is the value of \[\frac{\mathbf{1}}{\mathbf{2}}\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{36-21o}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{3+lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{15?}\]
  A)
   2                                 done clear
  B)
   3               done clear
  C)
   1 done clear
  D)
   0 done clear
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• question_answer30)
  What is the value of \[\left( \frac{\mathbf{1}}{\mathbf{2}}\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{25-2lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{4+lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{32+lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{1} \right)\]?
  A)
   0                                 done clear
  B)
   \[\frac{1}{5}\]              done clear
  C)
   1 done clear
  D)
   \[\frac{2}{5}\] done clear
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