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

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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 ${(\log_{p} q)}^{3} + {(\log_{q} r)}^{3} + {(\log_{r} p)}^{3}$ is -

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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 11

The solution set of the system of equations,

\log_{12} x (\frac{1}{\log_{x} 2} + \log_{2} y) = \log_{2} x

and

\log_{2} x \cdot (\log_{3} (x + y)) = 3 \log_{3} x

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 12

If

x_{1}

and

x_{2}

are the solution of the equation

x^{3 {\log^{3}}_{10} x - \frac{2}{3} \log_{10} x} = 100 \sqrt[3]{10}

then -

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 13

If

a^{x} = b, b^{y} = c, c^{z} = a

and

x = \log_{b} a^{2}; y = \log_{c} b^{3}

and

z = \log_{a} c^{k}

, where

a, b, c > 0

and

a, b, c \neq 1

then

k

is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 14

If

\log_{k} x \cdot \log_{5} k = \log_{x} 5, k \neq 1, k > 0,

then

x

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 15

If

x^{\frac{3}{4} {(\log_{3} x)}^{2} + \log_{3} x - \frac{5}{4}} = \sqrt{3}

then

x

has

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Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-2>Q 16

Integral real values of

x

satisfying

\log_{1 / 2} (x^{2} - 6 x + 12) \geq - 2

is

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

Statement-I : If

\log_{(\log_{5} x)} 5 = 2

, then

x = 5^{\sqrt{5}}

Because
Statement-II :

\log_{x} a = b

, if

a > 0

, then

x = a^{1 / b}

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

Compute the value of

\log_{\frac{1}{3}} \sqrt[4]{729 \cdot \sqrt[3]{9^{- 1} \cdot 27^{- \frac{4}{3}}}}