Embibe Experts Solutions for Chapter: Logarithm and Its Applications, Exercise 1: EXERCISE-1

Which one of the following denotes the greatest positive proper fraction?

The number of real solution of the equation ${\log }_{10}(7x-9{)}^2+{\log }_{10}(3x-4{)}^2=2$  is -

The equation, ${\log }_2\left(2x^2\right)+\left({\log }_{2}x\right)·x^{{\log }_x\left({\log }_{2}x+1\right)}+\frac{1}{2}{\log }_4^2\left(x^4\right)+2^{-3{\log }_{1/2}\left({\log }_{2}x\right)}=1$ has- 

Given system of simultaneous equations $2^x·5^y=1$ and $5^{x+1}. 2^y=2$. Then -

The value of $3^{{\log }_{4}5}+4^{{\log }_{5}3}-5^{{\log }_{4}3}-3^{{\log }_{5}4}$ is -

${\log }_{A}B$, where $B=\frac{12}{3+\sqrt{5}+\sqrt{8}}$ and $A=\sqrt{1}+\sqrt{2}+\sqrt{5}-\sqrt{10}$ is -

If  ${\log }_{c}2·{\log }_{b}625={\log }_{10}16·{\log }_{c}10$ where $c>0; c\ne 1; b>1; b\ne 1$  determine $b$ -

Number of cyphers after decimal before a significant figure comes in ${\left(\frac{5}{3}\right)}^{-100}$ is -