The equation $\frac{{\log }_8\left(\frac{8}{x^2}\right)}{{\left({\log }_{8}x\right)}^2}=3$ has -

Important Questions on Logarithm and Its Applications

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 3

Which of the following when simplified, vanishes?

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 4

Which of the following, when simplified, reduces to unity?

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 5

The number $N=\frac{1+2{\log }_{3}2}{{(1+{\log }_{3}2)}^2}+{\log }_6^{2}2$ when simplified reduces to -

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 6

Which of the following are correct?

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 7

If  $p, q\in N$  satisfy the equation $x^{\sqrt{x}}={\left(\sqrt{x}\right)}^x$ then $p$ & $q$ are -

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 8

The expression, ${\log }_p {\log }_p \underset{\begin{array}{ccc}n& radical& sign\end{array}}{\underbrace{\sqrt[p]{\sqrt[p]{\sqrt[p]{......\sqrt[p]{p}}}}}}$  where $p\ge 2, p\in N$, when simplified is -

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 9

Which of the following numbers are positive?

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 10

If  ${\log }_{p}q+{\log }_{q}r+{\log }_{r}p$ vanishes where $p, q$ and $r$ are positive reals different than unity then the value of ${\left({\log }_{p}q\right)}^3+{\left({\log }_{q}r\right)}^3+{\left({\log }_{r}p\right)}^3$ is -