G Tewani Solutions for Chapter: Logarithm and Its Applications, Exercise 3: DPP

The value of $X$ for which equation $5·3^{{\log }_{3}x}-2^{1-{\log }_{2}x}-3=0$

The sum of all values of $a$ satisfying the equation $\left|\begin{array}{cr}{\log }_{10}a& -1\\ {\log }_{10}\left(a-1\right)& 2\end{array}\right|={\log }_{10}a+{\log }_{10}2$ is

The number of real solution(s) of the equation $9^{{\log }_3\left({\log }_{e}x\right)}={\log }_{e}x-{\left({\log }_{e}x\right)}^2+1$ is equal to

The solution set of the equation $x^{{\log }_x{\left(1-x\right)}^2} = 9,$ is

The value of $x$ satisfying the equation ${\left(\sqrt{\pi }\right)}^{{\log }_{\pi }x}·{\left(\sqrt{\pi }\right)}^{{\log }_{{\pi }^2} x}·{\left(\sqrt{\pi }\right)}^{{\log }_{{\pi }^{4 }}x}·{\left(\sqrt{\pi }\right)}^{{\log }_{{\pi }^8 }x}$ ............... $\infty =3$ is equal to:

If $a>1, x>0$ and $2^{{\log }_a\left(2x\right)}=5^{{\log }_a\left(5x\right)}$, then $x$ is equal to:

If $x_1$ and $x_2$ are solution of the equation $\log \left({\log }_{64}\left|x\right|+{\left(25\right)}^x-\frac{1}{2}\right)=2x$, then

If ${\log }_{6}9-{\log }_{9}27+{\log }_{8}x={\log }_{64}x-{\log }_{6}4$, then the value of $x$ is