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

EASY

JEE Main/Advance

IMPORTANT

Earn 100

The number $N = \frac{1 + 2 \log_{3} 2}{{(1 + \log_{3} 2)}^{2}} + \log_{6}^{2} 2$ when simplified reduces to -

50% studentsanswered this correctly

Important Questions on Logarithm and Its Applications

HARD

JEE Main/Advance

IMPORTANT

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

Which of the following are correct?

MEDIUM

JEE Main/Advance

IMPORTANT

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}} = {(\sqrt{x})}^{x}

then

p

&

q

are -

HARD

JEE Main/Advance

IMPORTANT

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

The expression,

\log_{p} \log_{p} \underset{\begin{matrix} n & r a d i c a l & s i g n \end{matrix}}{\underset{⏟}{\sqrt[p]{\sqrt[p]{\sqrt[p]{. . . . . . \sqrt[p]{p}}}}}}

where

p \geq 2, p \in N

, when simplified is -

HARD

JEE Main/Advance

IMPORTANT

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

Which of the following numbers are positive?

HARD

JEE Main/Advance

IMPORTANT

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

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

is -

HARD

JEE Main/Advance

IMPORTANT

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 -

HARD

JEE Main/Advance

IMPORTANT

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 -

HARD

JEE Main/Advance

IMPORTANT

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 -