The value of $3^{{\log }_{4}5}+4^{{\log }_{5}3}-5^{{\log }_{4}3}-3^{{\log }_{5}4}$ is -

Important Questions on Logarithm and Its Applications

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-1>Q 12

Given that ${\log }_{p}x=\alpha$ and ${\log }_{q}x=\beta$  then value of ${\log }_{\frac{p}{q}}x$ equals-

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-1>Q 13

${\log }_{A}B$, where $B=\frac{12}{3+\sqrt{5}+\sqrt{8}}$ and $A=\sqrt{1}+\sqrt{2}+\sqrt{5}-\sqrt{10}$ is -

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-1>Q 14

If  ${\log }_{c}2·{\log }_{b}625={\log }_{10}16·{\log }_{c}10$ where $c>0; c\ne 1; b>1; b\ne 1$  determine $b$ -

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-1>Q 15

Number of cyphers after decimal before a significant figure comes in ${\left(\frac{5}{3}\right)}^{-100}$ is -

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 1

Which of the following when simplified reduces to an integer?

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

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

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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?