Embibe Experts Solutions for Chapter: Logarithm and Its Applications, Exercise 3: EXERCISE-3

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

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

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

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

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

The antilogarithm of $0.75$, if the base of the logarithm is $2401$ is

If $x, y>0, {\log }_{y}x+{\log }_{x}y=\frac{10}{3}$ and $xy=144$, then $\frac{x+y}{2}=\sqrt{N}$ where $N$ is a natural number, find the value of $N$.

Let $y=\sqrt{{\log }_{2}3·{\log }_{2}12·{\log }_{2}48·{\log }_{2}192+16}-{\log }_{2}12·{\log }_{2}48+10$. Then $y$ is