If $x^{\frac{3}{4} {\left({\log }_{3}x\right)}^2+{\log }_{3}x-\frac{5}{4}}= \sqrt{3}$ then $x$ has

Important Questions on Logarithm and Its Applications

MEDIUM

JEE Main/Advance

IMPORTANT

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

Integral real values of $x$ satisfying ${\log }_{1/2}\left(x^2-6x+12\right)\ge -2$ is

HARD

JEE Main/Advance

IMPORTANT

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

Statement-I : If  ${\log }_{\left({\log }_{5}x\right)}5=2$, then $x=5^{\sqrt{5}}$
Because
Statement-II : ${\log }_{x}a=b$, if $a>0$, then $x=a^{1/b}$

EASY

JEE Main/Advance

IMPORTANT

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

Compute the value of  ${\log }_{\frac{1}{3}}\sqrt[4]{729·\sqrt[3]{9^{-1}·{27}^{-\frac{4}{3}}}}$

EASY

JEE Main/Advance

IMPORTANT

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

The value of $x$ for which ${\log }_4{\log }_3{\log }_{2}x=0$, is

EASY

JEE Main/Advance

IMPORTANT

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

Find the value of ${49}^A+5^B$ where $A=1-{\log }_{7}2$and $B=-{\log }_{5}4$.

EASY

JEE Main/Advance

IMPORTANT

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

If $4^A+9^B={10}^C$, where $A={\log }_{16}4, B={\log }_{3}9$ and $C={\log }_{x}83$ then the value of $x$ is

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 3 - Logarithm and Its Applications>EXERCISE-3>Q 11

Find the value of the expression $\frac{6}{{\log }_4{\left(2000\right)}^6}+\frac{9}{{\log }_5{\left(2000\right)}^6}$

HARD

JEE Main/Advance

IMPORTANT

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

The value of $\frac{{81}^{\frac{1}{{\log }_{5}9}}+3^{\frac{3}{{\log }_{\sqrt{6}}3}}}{409}·\left((\sqrt{7}{)}^{\frac{2}{{\log }_{25}7}}-(125{)}^{{\log }_{25}6}\right)$ is