Logarithmic Equations

If ${\log }_{2}x=\frac{1}{3}.{\log }_{2}8-2{\log }_2\sqrt{3}$, then $x$ is equal to

If ${\mathrm{l}\mathrm{o}\mathrm{g}}_e{\mathrm{l}\mathrm{o}\mathrm{g}}_5\left[\sqrt{2x-2}+3\right]=0$ then the value of $x$ is-

The number of solution$\left(s\right)$ of the equation, $\log \left(-2x\right)=\log x^2$ is

Number of real values of $x$ which satisfy $\mathrm{l}\mathrm{o}{\mathrm{g}}_2{x}^2+{\log }_2\left(x+2\right)=4$ is/are

If $1-{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}5=\frac{1}{3}\left({\log }_{10}\frac{1}{2}+{\log }_{10}x+\frac{1}{3}{\log }_{10}5\right)$ then $x$ is equal to

${\log }_8+{\log }_8\left(x^2+\mathrm{x}-2\right)=\frac{4}{3} ,$ then$x$ is equal to-

Let $x, y$ be real numbers such that $x>2y>0$ and $2\log \left(x-2y\right)=\log x+\log y$. Then the possible value(s) of $\frac{x}{y}$

If ${\log }_{\left(2x+3\right)}\left(6x^2+23x+21\right)=4-{\log }_{\left(3x+7\right)}\left(4x^2+12x+9\right),$ then the value of $64x^2$ is

Which of the following is not the solution of ${\log }_{10}\left(x^2-2x+10\right)+{\log }_{10}\left(\frac{1}{x^2-2x}\right)=1-{\log }_{10}\left(x^2-2x\right)$?

The number of integral value of $x$ satisfying the equation $\left|{\log }_{\sqrt{3}}x-2\right|-\left|{\log }_{3}x-2\right|=2$ are

Number of real values of $x$ which satisfy $\mathrm{l}\mathrm{o}{\mathrm{g}}_2{x}^2+{\log }_2\left(x+2\right)=4$ is/are

If ${\log }_{y}x+ {\log }_{x}y= y,$ then $x + y =$

If  ${\left(a^{{\log }_{b}x}\right)}^2-5x^{{\log }_{b}a}+6=0$ where $a>0,b>0\mathrm{ }\&b\ne 1$, then the value of $x$ can be equal to

For the equation $1+{\mathrm{l}\mathrm{o}\mathrm{g}}_x\left(\frac{4-x}{10}\right)=\left({\mathrm{l}\mathrm{o}\mathrm{g}}_{10}\right({\mathrm{l}\mathrm{o}\mathrm{g}}_{10}p)-1){\mathrm{l}\mathrm{o}\mathrm{g}}_{x}10$ , match the value of p

given in column-II corresponding to the number of solutions given in column-I.
 

The number of solutions in $\left(–2\pi ,\mathrm{ }2\pi \right)$, for following equation ${\log }_2\left(\sin x\right)-{\log }_2\left|\cos x\right|+{\log }_3\tan x+{\log }_5\tan x=0$.

If 'x' is the solution of the equation

${\log }_{\left(3x+7 \right)}\left(4x^2+12x+9\right)+{\log }_{\left(2x+3\right)}\left(6x^2+23x+21\right)=4,$ then $\frac{1}{x^2}=$

If $\ln \left(x+z\right)+\ln \left(x-2y+z\right)=2\ln \left(x-z\right)$, then

${\left|x-1\right|}^{{\log }_3{x}^2-2{\log }_{x}9}={\left(x-1\right)}^7$, then the value of $x$ is

$x^{\left(\frac{3}{4}\right){\left({\log }_{2}x\right)}^2+{\log }_{2}x-\left(\frac{5}{4}\right) }=\sqrt{2}$ , then one of the values of $x$ is

If the sum of all solutions of the equation ${\left(x^{{\log }_{10}3}\right)}^2–\left(3^{{\log }_{10}x}\right)–2=0$ is $\left(a^{{\log }_{b}c}\right)$ where $b$ and $c$ are relatively prime and $a, b, c\in N.$ Then the value of $a+b+c$ is equal to-