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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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