Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-1>Q 14

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Number of integral solutions of inequality ${(\frac{1}{10})}^{\log_{(x - 3)} (x^{2} - 4 x + 3)} \geq 1$ are

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Important Questions on Logarithm and its Applications

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Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-1>Q 15

Solution set of the inequality

2 - \log_{2} (x^{2} + 3 x) \geq 0

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-1>Q 16

If

\log_{0.5} \log_{5} (x^{2} - 4) > \log_{0.5} 1,

then

x

lies in the interval

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Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-1>Q 17

If the solution set of the inequality

\log_{\sqrt{0.9}} \log_{5} (\sqrt{x^{2} + 5 + x}) > 0

contains

n

integral values, then

n

equals to

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Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-1>Q 18

Exhaustive set of values of

x

satisfying

\log_{|x|} (x^{2} + x + 1) \geq 0

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-1>Q 19

Complete solution set of the inequality

\sqrt{\log_{10}^{2} x - 1} > \log_{10} x - 1

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-1>Q 20

Find the domain of definition of the function

f (x) = \log_{10} (1 - \log_{10} (x^{2} - 5 x + 16))

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-1>Q 21

Range of

f (x) = \ln (3 x^{2} - 4 x + 5)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 1

If

k = \frac{\log (\sqrt{3^{\log_{3} 25} - 25^{\log_{5} 4}} + 1)}{\log (3 - \sqrt{3^{\log_{3} 5} - 5^{\log_{5} 4}})}

, then the value of

\log_{k} 512

is