9th Class Mathematics Related to Competitive Exam Question Bank

done Logarithms Total Questions - 40

• question_answer1)
  Evaluate: \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{4}}}\mathbf{3\times lo}{{\mathbf{g}}_{\mathbf{27}}}\mathbf{64}\]
  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: \[lo{{g}_{16}}64~-lo{{g}_{64}}16\]
  A)
   6                                 done clear
  B)
   \[\frac{1}{6}\] done clear
  C)
   \[\frac{6}{5}\]                          done clear
  D)
   \[\frac{5}{6}\] done clear
  View Solution play_arrow

• question_answer3)
  Find the value of x which satisfies the relation\[lo{{g}_{10}}2+lo{{g}_{10}}(\mathbf{4x}+1)=\mathbf{lo}{{\mathbf{g}}_{10}}(\mathbf{x}+1)+1\]
  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 log, 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)
  \[\frac{\log \sqrt[3]{6}}{\log 6}\]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)
   \[lo{{g}_{10}}10=0\]               done clear
  B)
   \[log\left( 2-3 \right)=log\left( 2\times 3 \right)\] done clear
  C)
   \[lo{{g}_{10}}1=1\]                 done clear
  D)
   \[log\left( 1\times 2\times 3 \right)=log1+log2+log3\] done clear
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• question_answer8)
  If \[{{\log }_{2}}\left[ {{\log }_{3}}\left( {{\log }_{2}}x \right) \right]=1\], 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)
  \[\log \mathbf{l60}\]is equal to:
  A)
   \[2\,log2+3\,log3\]         done clear
  B)
   \[3\,log2+2\,log3\] done clear
  C)
   \[3\,log2+2\,log3-log5\]            done clear
  D)
   \[5\,log2+log5\] done clear
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• question_answer10)
  If \[lo{{g}_{a}}(ab)=x,\]then \[lo{{g}_{b}}(ab)\]is:
  A)
   \[\frac{1}{x}\]                          done clear
  B)
   \[\frac{x}{1+x}\] done clear
  C)
   \[\frac{x}{1-x}\]                        done clear
  D)
   \[\frac{x}{x-1}\] done clear
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• question_answer11)
  If \[log2=x,log3=y\] and log\[\mathbf{7}=\mathbf{z}\], then the value of \[\mathbf{log}\left( \mathbf{8}.\sqrt[3]{\mathbf{21}} \right)\]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 \[lo{{g}_{8}}x+lo{{g}_{8}}\frac{1}{6}=\frac{1}{3}\], then the value of s Is:
  A)
   12      done clear
  B)
   16 done clear
  C)
   18                                done clear
  D)
   24 done clear
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• question_answer13)
  If \[lo{{g}_{5}}x+2{{\log }_{25}}x+3lo{{g}_{12}}x=9,\] 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 \[lo{{g}_{10}}5+lo{{g}_{10}}(5x+1)=log\left( x+5 \right)+1,\] 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 \[lo{{g}_{5}}({{x}^{2}}+x)-lo{{g}_{10}}(x+1)=2\], 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 \[\left( \frac{1}{{{\log }_{3}}60}+\frac{1}{{{\log }_{4}}60}+\frac{1}{{{\log }_{5}}60} \right)\]  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 \[\left( \mathbf{lo}{{\mathbf{g}}_{3}}\mathbf{4} \right)\left( \mathbf{lo}{{\mathbf{g}}_{4}}\mathbf{5} \right)\left( \mathbf{lo}{{\mathbf{g}}_{5}}\mathbf{6} \right)\left( \mathbf{lo}{{\mathbf{g}}_{6}}\mathbf{7} \right)\left( \mathbf{lo}{{\mathbf{g}}_{7}}\mathbf{8} \right)\left( \mathbf{lo}{{\mathbf{g}}_{8}}\mathbf{9} \right)\] 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 \[{{16}^{{{\log }_{4}}5}}\]is:
  A)
   \[\frac{5}{64}\]                             done clear
  B)
   5 done clear
  C)
   16                                done clear
  D)
   25 done clear
  View Solution play_arrow

• 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 \[lo{{g}_{10}}8=x\], then \[lo{{g}_{10}}\left( \frac{1}{80} \right)\] 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 \[x={{y}^{x}},y={{z}^{y}}\]and \[z={{x}^{y}}\], 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)
  \[\frac{\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{6}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{2+1}}=\]
  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
  View Solution play_arrow

• question_answer23)
  If \[\mathbf{x=lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{27}\] and \[\mathbf{y=lo}{{\mathbf{g}}_{\mathbf{9}}}\mathbf{27}\] 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
  View Solution play_arrow

• question_answer24)
  If \[l\mathbf{og}\left( \mathbf{0}.\mathbf{37} \right)=\overline{1}.\mathbf{756}\], 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)
   \[\overline{1}.146\] done clear
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• question_answer25)
  The value of \[\frac{1}{1+{{\log }_{ab}}c}+\frac{1}{1+{{\log }_{ac}}b}+\frac{1}{1+{{\log }_{bc}}a}\] 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\[{{2}^{lo{{g}_{3}}^{9}}}+{{25}^{lo{{g}_{9}}^{3}}}={{8}^{lo{{g}_{x}}^{9}}}\], 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 \[lo{{g}_{10}}\left( \frac{3}{2} \right)+lo{{g}_{10}}\left( \frac{4}{3} \right)+lo{{g}_{10}}\left( \frac{5}{4} \right)+.......\]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 \[{{[lo{{g}_{10}}(5lo{{g}_{10}}100)]}^{2}}_{b}\]
  A)
   4                     done clear
  B)
   3              done clear
  C)
   2                                 done clear
  D)
   1 done clear
  View Solution play_arrow

• question_answer29)
  What is the value of \[\frac{1}{2}lo{{g}_{10}}36-21o{{g}_{10}}3+lo{{g}_{10}}15?\]
  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 \[\left( \frac{1}{2}1o{{g}_{10}}25-2lo{{g}_{10}}4+lo{{g}_{10}}32+lo{{g}_{10}}1 \right)\]?
  A)
   0                                 done clear
  B)
   \[\frac{1}{5}\]              done clear
  C)
   1       done clear
  D)
   \[\frac{2}{5}\] done clear
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• question_answer31)
  What is the value of\[[lo{{g}_{12}}(10)]/[lo{{g}_{144}}(10)]\]?
  A)
   \[\frac{1}{2}\]                          done clear
  B)
   2     done clear
  C)
   1                                 done clear
  D)
   \[lo{{g}_{10}}13\] done clear
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• question_answer32)
  If \[{{\log }_{r}}6=m\] and \[lo{{g}_{r}}3=n\] then is \[lo{{g}_{r}}\left( r/2 \right)\]is equal to
  A)
   \[m-n+1\]         done clear
  B)
   \[m+n-1\]            done clear
  C)
   \[m-n-1\]                       done clear
  D)
   \[m-n+1\] done clear
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• question_answer33)
  What is the value of\[\mathbf{2}\,\mathbf{log}(\mathbf{5}/\mathbf{8})+\mathbf{log}\left( \mathbf{l28}/\mathbf{125} \right)+\mathbf{log}\left( \mathbf{5}/\mathbf{2} \right)\]?
  A)
   0        done clear
  B)
   -1              done clear
  C)
   2                                 done clear
  D)
   5 done clear
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• question_answer34)
  What is the value of \[lo{{g}_{100}}0.01\]?
  A)
   1/2                               done clear
  B)
  : \[-1\]   done clear
  C)
   \[\frac{-1}{3}\]                         done clear
  D)
   -3 done clear
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• question_answer35)
  What is the valve of \[\left( lo{{g}_{\frac{1}{2}}}2 \right)\left( lo{{g}_{\frac{1}{3}}}3 \right)\left( lo{{g}_{\frac{1}{4}}}4 \right)........\left( lo{{g}_{\frac{1}{99}}}99 \right)\]
  A)
   1  done clear
  B)
   -1              done clear
  C)
   1 or -1                          done clear
  D)
   0 done clear
  View Solution play_arrow

• question_answer36)
  Which is greatest among the following?
  A)
   \[lo{{g}_{2}}20\]  done clear
  B)
   \[lo{{g}_{7}}35\]          done clear
  C)
   \[lo{{g}_{5}}70\]                      done clear
  D)
   \[lo{{g}_{3}}68\] done clear
  View Solution play_arrow

• question_answer37)
  If \[\frac{\log x}{\log y}=\frac{\log 64}{\log 8}\], then the relation between x and \[\gamma \] is.
  A)
   \[x=\sqrt{y}\]                           done clear
  B)
   \[x={{y}^{3}}\]           done clear
  C)
   \[y={{x}^{2}}\]                     done clear
  D)
   \[x={{y}^{2}}\] done clear
  View Solution play_arrow

• question_answer38)
  If \[\mathbf{lo}{{\mathbf{g}}_{3}}\mathbf{2}=\mathbf{x}\] then the value of \[\frac{\mathbf{lo}{{\mathbf{g}}_{10}}7\mathbf{2}}{\mathbf{lo}{{\mathbf{g}}_{10}}\mathbf{2}4}\] Is
  A)
   \[\frac{1+x}{1-x}\]                   done clear
  B)
   \[\frac{2+3x}{1+3x}\] done clear
  C)
   \[\frac{2-3x}{2+3x}\]                done clear
  D)
   \[\frac{3x+1}{3x+2}\] done clear
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• question_answer39)
  \[log\left( \frac{1}{2} \right)+log\left( \frac{2}{3} \right)+log\left( \frac{3}{4} \right)+......+log\left( \frac{999}{10000} \right)\text{= }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{ }\text{.}\]
  A)
   \[-3\]       done clear
  B)
   \[-1\]             done clear
  C)
   0                                 done clear
  D)
   2 done clear
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• question_answer40)
  \[{{\log }_{2}}1.\,{{\log }_{3}}2.\,{{\log }_{4}}3\,.\,lo{{g}_{5}}4\,.\,lo{{g}_{6}}5....{{\log }_{100}}99\]\[=\_\_\_\_\_.\]
  A)
   \[\infty \]                                   done clear
  B)
   0 done clear
  C)
   1                                 done clear
  D)
   Cannot be determined done clear
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