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question_answer1)
Expansion of \[\mathbf{log}{{\mathbf{~}}_{\mathbf{3}}}\left( \frac{\mathbf{27}{{\mathbf{x}}^{\mathbf{3}}}}{\mathbf{5}} \right)\] equals to E, then \[\frac{\mathbf{E}}{\mathbf{3}}\] is ________
A)
\[1+{{\log }_{3}}x-\frac{1}{3}{{\log }_{3}}5\] done
clear
B)
\[3+3\text{ }{{\log }_{3}}x+{{\log }_{3}}5\] done
clear
C)
\[1+\text{lo}{{\text{g}}_{3}}x+\text{lo}{{\text{g}}_{3}}5\] done
clear
D)
\[{{\log }_{3}}x+\frac{1}{3}\text{lo}{{\text{g}}_{3}}5\] done
clear
E)
None of these done
clear
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question_answer2)
Simplification of\[\mathbf{5}\text{ }\mathbf{log}\text{ }\mathbf{2}+\mathbf{4}\text{ }\mathbf{log}\text{ }\mathbf{3}+\mathbf{2}\text{ }\mathbf{log}\text{ }\mathbf{4}\] \[+\,\mathbf{log}\text{ }\mathbf{5}-\mathbf{2}\text{ }\mathbf{log}\text{ }\mathbf{9}\]is ________
A)
\[\text{log 2156}\] done
clear
B)
\[\text{log 256}\] done
clear
C)
\[\text{log 2560}\] done
clear
D)
\[\text{log 3162}\] done
clear
E)
None of these done
clear
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question_answer3)
Which of the following statements is not correct?
A)
\[{{\log }_{8}}512=3\] done
clear
B)
\[{{\log }_{10}}0.001=-\,3\] done
clear
C)
\[{{\log }_{5}}125=\frac{{{\log }_{1}}125}{{{\log }_{1}}125}\] done
clear
D)
\[{{\log }_{2}}1=0\] done
clear
E)
None of these done
clear
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question_answer4)
Find the value of \[\mathbf{lo}{{\mathbf{g}}_{\frac{\mathbf{1}}{\mathbf{6}}}}\mathbf{ 216}\sqrt{\mathbf{6}}\]
A)
\[\frac{-5}{2}\] done
clear
B)
\[\frac{-7}{2}\] done
clear
C)
\[\frac{-3}{2}\] done
clear
D)
\[\frac{5}{2}\] done
clear
E)
None of these done
clear
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question_answer5)
If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{27}\sqrt{\mathbf{3}}}}\mathbf{ 729=x}\], then log x equals to:
A)
\[\log \left( \frac{5}{2} \right)\] done
clear
B)
\[\log \left( \frac{7}{12} \right)\] done
clear
C)
\[\log \left( \frac{2}{5} \right)\] done
clear
D)
\[\log \left( \frac{12}{7} \right)\] done
clear
E)
None of these done
clear
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question_answer6)
If \[\mathbf{x}>\mathbf{1}\]and \[\mathbf{a}>\mathbf{1},\] then \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{a}}}\mathbf{x}\] is _______
A)
positive done
clear
B)
negative done
clear
C)
zero done
clear
D)
both positive and negative done
clear
E)
None of these done
clear
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question_answer7)
If a > 1 and \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{a}}}\mathbf{x}\] is negative them _______
A)
\[x>0\] done
clear
B)
\[x>1\] done
clear
C)
\[-\,1<x<1\] done
clear
D)
\[0<x<1\] done
clear
E)
None of these done
clear
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question_answer8)
For \[x>1\] and \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{b}}}\mathbf{x}\] is negative, then:
A)
\[b>0\] done
clear
B)
\[0<b<1\] done
clear
C)
\[b<0\] done
clear
D)
\[-\text{ }1<b<1\] done
clear
E)
None of these done
clear
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question_answer9)
Which among the following statements is incorrect?
A)
\[{{\log }_{7}}3.{{\log }_{27}}4.\,{{\log }_{5}}7.{{\log }_{64}}5\] done
clear
B)
\[{{\log }_{\frac{3}{7}}}\text{ }2.\overline{3}=-1\] done
clear
C)
\[lo{{g}_{3-{{\sqrt{8}}^{3+\sqrt{8}}}}}=-1~\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer10)
If \[{{\mathbf{a}}^{\mathbf{6}}}=\text{ }{{\mathbf{b}}^{\mathbf{6}}}+{{\mathbf{c}}^{\mathbf{6}}}\], then the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{c}}}({{\mathbf{a}}^{\mathbf{2}}}-{{\mathbf{b}}^{\mathbf{2}}})+\mathbf{lo}{{\mathbf{g}}_{\mathbf{c}}}({{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}+\mathbf{ab})\]\[+\text{ }\mathbf{lo}{{\mathbf{g}}_{\mathbf{c}}}\left( {{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}+\mathbf{ab} \right)\] is equal to ________
A)
1 done
clear
B)
3 done
clear
C)
6 done
clear
D)
0 done
clear
E)
None of these done
clear
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question_answer11)
If \[\frac{\mathbf{log x}}{\mathbf{log y}}\mathbf{=}\frac{\mathbf{log 121}}{\mathbf{log 11}}\], then the relation between x and Y is __________
A)
\[x=\sqrt{y}\] done
clear
B)
\[{{x}^{2}}=y\] done
clear
C)
\[x={{y}^{2}}\] done
clear
D)
\[x=2y\] done
clear
E)
None of these done
clear
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question_answer12)
If \[\log \,(x+3)-\log \,(2x-5)=1,\]then the value of \[x\] is ________
A)
\[1\frac{15}{19}\] done
clear
B)
\[2\frac{15}{19}\] done
clear
C)
8 done
clear
D)
4 done
clear
E)
None of these done
clear
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question_answer13)
Which of the following is least among the following? |
\[\text{lo}{{\text{g}}_{4}}260,\,\,{{\log }_{2}}18,\,\,{{\log }_{7}}2300,\,\,{{\log }_{5}}630,\,\,{{\log }_{3}}200\] |
A)
\[{{\log }_{4}}260\] done
clear
B)
\[{{\log }_{2}}18\] done
clear
C)
\[{{\log }_{7}}2300\] done
clear
D)
\[{{\log }_{3}}225\] done
clear
E)
None of these done
clear
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question_answer14)
The value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{7}}}\mathbf{3}.\text{ }\mathbf{lo}{{\mathbf{g}}_{\mathbf{27}}}\mathbf{4}.\text{ }\mathbf{lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{7}.\text{ }\mathbf{lo}{{\mathbf{g}}_{\mathbf{64}}}\mathbf{5}\]is _________
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{1}{4}\] done
clear
C)
\[\,\frac{1}{8}\] done
clear
D)
\[\frac{1}{9}\] done
clear
E)
None of these done
clear
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question_answer15)
Solve: \[\frac{\mathbf{lo}{{\mathbf{g}}_{\mathbf{16}}}\mathbf{(lo}{{\mathbf{g}}_{\mathbf{5}}}\mathbf{ 625)}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{512}}}\mathbf{(lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{ 6561)}}\]
A)
\[\frac{1}{6}\] done
clear
B)
\[\frac{5}{2}\] done
clear
C)
\[\frac{2}{3}\] done
clear
D)
\[\frac{3}{2}\] done
clear
E)
None of these done
clear
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question_answer16)
\[{{\mathbf{2}}^{\mathbf{4}\,\mathbf{log}}}{{^{_{\mathbf{2}}}}^{\mathbf{5}}}\mathbf{ + }{{\mathbf{3}}^{\mathbf{2}\,\mathbf{log}}}{{^{_{\mathbf{3}}}}^{\mathbf{4}}}\mathbf{=}\]________
A)
641 done
clear
B)
5 done
clear
C)
25 done
clear
D)
625 done
clear
E)
None of these done
clear
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question_answer17)
If \[\mathbf{log}\,\mathbf{[4}-\mathbf{6 lo}{{\mathbf{g}}_{\mathbf{64}}}\mathbf{ (x+5)]=0}\], then the value of x is _______
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
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question_answer18)
If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{4 + lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{7=x }-\mathbf{ 1}\], then find the value of\[\frac{\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{ 84}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{ 28}}\].
A)
\[\frac{x}{x+1}\] done
clear
B)
\[\frac{x+1}{x}\] done
clear
C)
\[\frac{x-1}{x}\] done
clear
D)
\[\frac{x}{x-1}\] done
clear
E)
None of these done
clear
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question_answer19)
If \[{{\mathbf{x}}^{\mathbf{3}}}\mathbf{-}{{\mathbf{y}}^{\mathbf{3}}}\mathbf{=1}\], x > y, then find the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{(x-y)}}}\mathbf{ (}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+xy)}\]
A)
0 done
clear
B)
1 done
clear
C)
-1 done
clear
D)
Cannot be determined done
clear
E)
None of these done
clear
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question_answer20)
\[\mathbf{log}\left( \frac{\mathbf{1}}{\mathbf{2}} \right)\mathbf{+log}\left( \frac{\mathbf{2}}{\mathbf{3}} \right)\mathbf{+log}\left( \frac{\mathbf{3}}{\mathbf{4}} \right)......\mathbf{+log}\left( \frac{\mathbf{999}}{\mathbf{1000}} \right)\]
A)
-3 done
clear
B)
-2 done
clear
C)
-1 done
clear
D)
0 done
clear
E)
None of these done
clear
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question_answer21)
If \[{{\mathbf{5}}^{\mathbf{log}}}{{^{_{\mathbf{5}}}}^{\mathbf{4}}}\mathbf{+}{{\mathbf{4}}^{\mathbf{lo}{{\mathbf{g}}_{\mathbf{x}}}\mathbf{3}}}\mathbf{=7}\] then the value of x is _________
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
E)
None of these done
clear
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question_answer22)
If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{x}-\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{y}=\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{5}-\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{10}\] and \[\mathbf{3x=y+2}\]then y is equal to _________
A)
4 done
clear
B)
3 done
clear
C)
2 done
clear
D)
1 done
clear
E)
None of these done
clear
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question_answer23)
Find the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\left( \frac{{{\mathbf{2}}^{\mathbf{2}}}\times {{\mathbf{3}}^{\mathbf{3}}}}{{{\mathbf{5}}^{\mathbf{3}}}} \right)\] where it is given that \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{2=0}\mathbf{.3010}\]and \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{3=0}\mathbf{.4771}\]
A)
0.2373 done
clear
B)
2.0970 done
clear
C)
0.2070 done
clear
D)
0.2273 done
clear
E)
None of these done
clear
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question_answer24)
Solve for x, the equation: \[\mathbf{log}\,\,\left[ \mathbf{log}\,\mathbf{3}+\mathbf{log}\,\mathbf{3}\,\left( \mathbf{x}+\mathbf{1} \right) \right]=\mathbf{0}\]
A)
\[{{2}^{8}}+1\] done
clear
B)
\[{{3}^{8}}+1\] done
clear
C)
\[{{2}^{7}}-1\] done
clear
D)
\[{{3}^{7}}-1\] done
clear
E)
None of these done
clear
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question_answer25)
If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{x}}}\mathbf{1/32=}\frac{-\,\mathbf{5}}{\mathbf{4}}\] then the value of x is __________
A)
8 done
clear
B)
16 done
clear
C)
32 done
clear
D)
64 done
clear
E)
None of these done
clear
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question_answer26)
If \[\mathbf{4a}\mathbf{.}{{\mathbf{b}}^{\mathbf{5log}}}{{_{\mathbf{b}}}^{\mathbf{a}}}\mathbf{=2916}\]then the value of a is _________
A)
1 done
clear
B)
0 done
clear
C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
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question_answer27)
If log 2 = 0.3010, then the number of digits in \[{{\mathbf{2}}^{\mathbf{512}}}\] is _______
A)
150 done
clear
B)
154 done
clear
C)
155 done
clear
D)
153 done
clear
E)
None of these done
clear
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question_answer28)
The value of \[\frac{\mathbf{2}}{\mathbf{1+2lo}{{\mathbf{g}}_{{{\mathbf{a}}^{\mathbf{2}}}{{\mathbf{b}}^{\mathbf{2}}}}}\mathbf{c}}\mathbf{+ }\frac{\mathbf{2}}{\mathbf{1+2lo}{{\mathbf{g}}_{{{\mathbf{a}}^{\mathbf{2}}}{{\mathbf{c}}^{\mathbf{2}}}}}\mathbf{b}}\]+\[\frac{\mathbf{2}}{\mathbf{1+2lo}{{\mathbf{g}}_{{{\mathbf{b}}^{\mathbf{2}}}{{\mathbf{c}}^{\mathbf{2}}}}}\mathbf{a}}\mathbf{ }\]is equal to _________
A)
2 done
clear
B)
4 done
clear
C)
1 done
clear
D)
\[\text{log }{{a}^{2}}{{b}^{2}}{{c}^{2}}\] done
clear
E)
None of these done
clear
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question_answer29)
Which one of the following statements is true?
A)
\[{{\log }_{5}}\sqrt{5\sqrt{5\sqrt{5........\infty }}}=1\] done
clear
B)
If \[{{5}^{\text{lo}{{\text{g}}_{5}}x}}+3x-12=0\], then \[x=6\] done
clear
C)
If \[{{3}^{{{\log }_{3}}}}^{(x-5)}+3(x-5)-4=0\], then\[x=3\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer30)
If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{16}}}\mathbf{m}=\mathbf{4}.\mathbf{5}\] and \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{4}}}\mathbf{n}=\mathbf{9},\]then m = ________
A)
\[\sqrt{n}\] done
clear
B)
\[{{n}^{2}}\] done
clear
C)
n done
clear
D)
\[n\sqrt{n}\] done
clear
E)
None of these done
clear
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question_answer31)
The value of the expression \[{{\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{2} \right)}^{\mathbf{3}}}\mathbf{+}\] \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{8}\,.\,\mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{5}\text{ }\mathbf{+}\text{ }{{\left( \mathbf{lo}{{\mathbf{g}}_{\mathbf{10}}}\mathbf{5} \right)}^{\mathbf{3}}}\] is equal to _______
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
E)
None of these done
clear
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question_answer32)
\[\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{3}}}\mathbf{x}}\mathbf{.}\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{x}}}\mathbf{27}}\mathbf{.}\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{9}}}\mathbf{x}}\mathbf{.}\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{x}}}\mathbf{729}}\]
A)
\[\frac{1}{3}\] done
clear
B)
3 done
clear
C)
9 done
clear
D)
\[\frac{1}{9}\] done
clear
E)
None of these done
clear
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question_answer33)
If the sum of two numbers m and n is\[\sqrt{\mathbf{22}}\] and their difference is \[\sqrt{\mathbf{18}}\] (where m > n), then the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{m}}}\mathbf{n}\] is equal to _____
A)
1 done
clear
B)
0 done
clear
C)
\[-1\] done
clear
D)
2 done
clear
E)
None of these done
clear
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question_answer34)
If \[\mathbf{x=}\frac{\sqrt{\mathbf{8}}\mathbf{+}\sqrt{\mathbf{2}}}{\mathbf{2}}\] and \[\mathbf{y=}\frac{\sqrt{\mathbf{8}}-\sqrt{\mathbf{2}}}{\mathbf{2}}\] then the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{121}}}\], \[\mathbf{(}{{\mathbf{x}}_{\mathbf{2}}}\mathbf{+4xy+}{{\mathbf{y}}_{\mathbf{2}}}\mathbf{)}\], equal to __________
A)
1 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{13}{4}\] done
clear
D)
2 done
clear
E)
None of these done
clear
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question_answer35)
If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{(}{{\mathbf{a}}^{\mathbf{2}}}-{{\mathbf{b}}^{\mathbf{2}}}\mathbf{)}}}\left( {{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}-\mathbf{2ab} \right)\] then find the value of.
A)
0 done
clear
B)
1 done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[\frac{1}{2}\] done
clear
E)
None of these done
clear
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question_answer36)
\[{{\mathbf{3}}^{\frac{\mathbf{2}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{32}}}\mathbf{9}}}}\mathbf{+}{{\mathbf{8}}^{\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{25}}}\mathbf{4}}}}\mathbf{+}{{\mathbf{4}}^{\frac{\mathbf{1}}{\mathbf{lo}{{\mathbf{g}}_{\mathbf{27}}}\mathbf{2}}}}\]= ________
A)
729 done
clear
B)
150 done
clear
C)
886 done
clear
D)
782 done
clear
E)
None of these done
clear
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question_answer37)
If \[{{\mathbf{2}}^{\mathbf{a}}}={{\left( \mathbf{0}.\mathbf{02} \right)}^{\mathbf{b}}}=\mathbf{100}\], then the value of \[\frac{\mathbf{1}}{\mathbf{a}}-\frac{\mathbf{1}}{\mathbf{b}}\] is equal to _________
A)
0 done
clear
B)
1 done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{1}{4}\] done
clear
E)
None of these done
clear
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question_answer38)
If \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{54}}}\mathbf{16}=\mathbf{a}\], then find the value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{36}}}\mathbf{3}\].
A)
\[\frac{8+2a}{2-a}\] done
clear
B)
\[\frac{4-a}{8+4a}\] done
clear
C)
\[\frac{2-a}{8+2a}\] done
clear
D)
\[\frac{8+4a}{4-a}\] done
clear
E)
None of these done
clear
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question_answer39)
The value\[\sqrt{\mathbf{3}\sqrt{\mathbf{3}\sqrt{\mathbf{3}......}}}\mathbf{+log}\sqrt{\mathbf{7}\sqrt{\mathbf{7}\sqrt{\mathbf{7}......}}}\] is equal to _______
A)
0 done
clear
B)
1 done
clear
C)
2 done
clear
D)
log 21 done
clear
E)
None of these done
clear
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question_answer40)
Find the value of\[^{\mathbf{3}}\sqrt{\mathbf{44}\mathbf{.59}}\] approximately.
A)
2.546 done
clear
B)
3.546 done
clear
C)
2.8936 done
clear
D)
3.245 done
clear
E)
None of these done
clear
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