Logarithm - Aptitude MCQ Questions and Solutions with Explanations

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31.
$$\frac{1}{2}\left( {\log x + \log y} \right)$$    will equal to $$\log \left( {\frac{{x + y}}{2}} \right)$$   if -

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32.
If $$\log \frac{a}{b} + \log \frac{b}{a} = $$   $$\,\log \left( {a + b} \right),$$   then -

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33.
$${\log \left( {\frac{{{a^2}}}{{bc}}} \right) + }$$   $${\log \left( {\frac{{{b^2}}}{{ac}}} \right) + }$$   $${\log \left( {\frac{{{c^2}}}{{ab}}} \right)}$$   is equal to -

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34.
$$\frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}}$$     is equal to -

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35.
$${\frac{1}{{\left( {{{\log }_a}bc} \right) + 1}} + }$$   $${\frac{1}{{\left( {{{\log }_b}ca} \right) + 1}} + }$$   $${\frac{1}{{\left( {{{\log }_c}ab} \right) + 1}}}$$   is equal to -

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36.
If $${\log _{10}}7 = a,$$   then $${\log _{10}}\left( {\frac{1}{{70}}} \right)$$   is equal to -

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37.
If $$\log x - 5\log 3 = - 2,$$     then x equals -

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38.
If $$a = {b^2} = {c^3} = {d^4},$$    then the value of $${\log _a}\left( {abcd} \right)$$   would be -

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39.
If $${\log _3}x + {\log _{9}}{x^2} + {\log _{27}}{x^3}$$     $$ = 9,$$  then x equals to -

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40.
If $${\log _7}{\log _5}\left( {\sqrt {x + 5} + \sqrt x } \right)$$     $$ = 0,$$  what is the value of x ?

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