Logarithmic Equations and Inequalities

If ${\log }_{8}x+{\log }_{4}x+{\log }_{2}x=11,x=$ ?

Consider the inequality ${\log }_x\left(\frac{15}{1-2x}\right)<-2.$ Which of the following is/are CORRECT?

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

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 $\frac{1}{x^2}=$

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

${\log }_{x-1}\left(4\right)=1+{\log }_2\left(x-1\right)$, then the values of $x$, will be

If ${\log }_4{\log }_3{\log }_{2}x=0$, then the value of $x$ is.

$9^{1+\log x}-3^{\left(1+\log x\right)}-210=0$, then the value of $x$, is (where base of $\log$ is $3$).

Let $f$ be a function defined on the set of all positive integers such that $f\left(xy\right)=f\left(x\right)+f\left(y\right)$ for all positive integers $x, y.$ If $f\left(12\right)=24$ and $f\left(8\right)=15$ , the value of $f\left(48\right)$ is

If ${\log }_2\left(a+b\right)+{\log }_2\left(c+d\right)\ge 4$. Then the min. value of the expression $a+b+c+d$ is

The solution set of the inequality ${\log }_{{\left(\cos x\right)}^2}\left(3-2x\right)<{\log }_{{\left(\cos x\right)}^2}\left(2x-1\right)$ is

Set of all the values of $x$ satisfying the inequality ${\log }_{x+\frac{1}{x}}\left({\log }_2\frac{x-1}{x+2}\right)>0$ is

The least integer $a$, for which $1+{\log }_5\left(x^2+1\right)\le {\log }_5\left(a{x}^2+4x+a\right)$ is true for all $x\in R$ is-

Solution of the in equation ${\log }_{0.1}\left({\log }_2\frac{x^2+1}{\left|x-1\right|}\right)<0$ contains the interval

The set of real values of $x$ for which ${\log }_{0.2}\frac{x+2}{x} \le 1$ is

If ${\log }_{0.04}\left(x-1\right)\ge {\log }_{0.2}\left(x-1\right)$ then $x$ belongs to the interval

The set of real values of $x$ for which $2^{{\log }_{\sqrt{2}}\left(x-1\right)}>x+5$ is

If ${\log }_{\frac{1}{\sqrt{2}}}\sin x>0, x\in \left[0, 4\pi \right]$, then the number of values of $x$, which are integral multiples of $\frac{\pi }{4}$ is.