The equation $x^{\left[{\left({\log }_{3}x\right)}^2 -\frac{9}{2}{\log }_{3}x+5\right]}=3\sqrt{3}$ has

Important Questions on Logarithm and its Applications

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 7

The possible solution of ordered pair $\left(x,y\right)$ of the system of equations ${\log }_{3}x+{\log }_{3}y=2+{\log }_{3}2$ and ${\log }_{27}\left(x+y\right)=\frac{2}{3}$

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 8

The value of $x$ for ${\log }_{2}x·{\log }_{3}x·{\log }_{5}x={\log }_{2}x·{\log }_{3}x+{\log }_{3}x·{\log }_{5}x+{\log }_{5}x·{\log }_{2}x$

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 9

If $a$ and $b$ are the solutions of equation ${\log }_5\left({\log }_{64}\left|x\right|-\frac{1}{2}+{25}^x\right)=2x$ then

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 10

If $\frac{1}{2}\le {\log }_{0.1}x\le 2,$ then

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 11

Which of the following is correct?

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 12

The domain of the function $f\left(x\right)={\log }_{1/2}\left(-{\log }_2\left(1+\frac{1}{\sqrt[4]{x}}\right)-1\right)$ is

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 13

If ${\mathrm{q}}^2-4\mathrm{pr}=0,\mathrm{p}>0,$ then the domain of the function $\mathrm{f}\left(\mathrm{x}\right)=\log \left({\mathrm{px}}^3+(\mathrm{p}+\mathrm{q}){\mathrm{x}}^2+(\mathrm{q}+r)x+r\right)$ is

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 14

The range of the function $f\left(x\right)={\log }_{\sqrt{2}}\left(2-{\log }_2\left(16{\sin }^{2}x+1\right)\right)$ is