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

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The solution set of the inequality $\frac{(3^{x} - 4^{x}) \cdot \ln (x + 2)}{x^{2} - 3 x - 4} \leq 0$ is

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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-2>Q 4

Let

α = \log_{10} 15

and

β = \log_{10} 16

. If a set

A = \{\log_{10} 1, \log_{10} 2, \dots \dots \dots \log_{10} 50\}

, then find the number of elements in set

A

which can be written in the form of

a α + b β + c

(where

a, b

and

c

are rational numbers and

a, b, c > 0

).

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Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 5

The equation

\log_{x^{2}} 16 + \log_{2 x} 64 = 3

has

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Alpha Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and its Applications>Exercise-2>Q 6

The equation

x^{[{(\log_{3} x)}^{2} - \frac{9}{2} \log_{3} x + 5]} = 3 \sqrt{3}

has

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

The possible solution of ordered pair

(x, y)

of the system of equations

\log_{3} x + \log_{3} y = 2 + \log_{3} 2

and

\log_{27} (x + y) = \frac{2}{3}

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

The value of

x

for

\log_{2} x \cdot \log_{3} x \cdot \log_{5} x = \log_{2} x \cdot \log_{3} x + \log_{3} x \cdot \log_{5} x + \log_{5} x \cdot \log_{2} x

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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} (\log_{64} | x | - \frac{1}{2} + 25^{x}) = 2 x

then

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

If

\frac{1}{2} \leq \log_{0.1} x \leq 2,

then

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

Which of the following is correct?