Q.1
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
Q.2
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 -
Q.3
If $${\log _{10}}a = p,$$   $${\log _{10}}b = q,$$   then what is $${\log _{10}}\left( {{a^p}{b^q}} \right)$$   equal to?
Q.4
If $$\log 2 = 0.3010\,$$   and $$\log 3 = 0.4771,\,$$   the value of $${\log _5}512$$   = ?
Q.5
If the logarithm of a number is - 3.153, what are characteristic and mantissa?
Q.6
If $${\log _{10}}7 = a,$$   then $${\log _{10}}\left( {\frac{1}{{70}}} \right)$$   is equal to -
Q.7
If $$\log x - 5\log 3 = - 2,$$     then x equals -
Q.8
If $$\log 2 = 0.30103,$$    the number of digits in $${4^{50}}$$ is -
Q.9
The number of digits in $${{\text{4}}^9} \times {{\text{5}}^{17}}{\text{,}}$$   when expressed in usual form, is -
Q.10
$$\frac{1}{2}\left( {\log x + \log y} \right)$$    will equal to $$\log \left( {\frac{{x + y}}{2}} \right)$$   if -
Q.11
If $$\log \frac{a}{b} + \log \frac{b}{a} = $$   $$\,\log \left( {a + b} \right),$$   then -
Q.12
If $$a = {b^2} = {c^3} = {d^4},$$    then the value of $${\log _a}\left( {abcd} \right)$$   would be -
Q.13
If $${\log _3}x + {\log _{9}}{x^2} + {\log _{27}}{x^3}$$     $$ = 9,$$  then x equals to -
Q.14
If $${\log _7}{\log _5}\left( {\sqrt {x + 5} + \sqrt x } \right)$$     $$ = 0,$$  what is the value of x ?
Q.15
If $${\log _{10000}}x = - \frac{1}{4}{\text{,}}$$    then the value of x is = ?
Q.16
$$\frac{{\log \sqrt 8 }}{{\log 8}}\,\,{\text{is equal to = ?}}$$
Q.17
$${\log \left( {\frac{{{a^2}}}{{bc}}} \right) + }$$   $${\log \left( {\frac{{{b^2}}}{{ac}}} \right) + }$$   $${\log \left( {\frac{{{c^2}}}{{ab}}} \right)}$$   is equal to -
Q.18
$$\frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}}$$     is equal to -
Q.19
$$2{\log _{10}}^5 + $$  $${\log _{10}}8 \,- $$  $$\frac{1}{2}{\log _{10}}4$$   = ?
Q.20
If $${\log _a}\left( {ab} \right) = x{\text{,}}\,$$   then $${\log _b}\left( {ab} \right)$$   is -
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