Solving Exponential Equations

If ${\log }_{x}a, a^x$ and ${\log }_{b}x$ are in $GP$, then what is $x$ equal to?

Let $\frac{{\log }_x\left(2a-x\right)}{{\log }_x\left(2\right)}+\frac{{\log }_a\left(x\right)}{{\log }_a\left(2\right)}=\frac{1}{{\log }_{a^2-1}\left(2\right)}$, then sum of possible value(s) of '$a$' for which equation has only one solution will lie in interval

${\log }_{0.01}\left(10,000\right)=x$; Find the value of $x$?

Solve the following exponential equation by trial and improvement method.

$\frac{2^{3x}}{8}=4^x$

Solve the following exponential equation by trial and improvement method.

$\frac{3^{5x}}{27}={27}^x$

Solve the following exponential equation by inspection method.

$\frac{3^{6x}}{3^6}={81}^x$

Solve the following exponential equation by inspection method.

$\frac{5^{3x}}{5^6}=\frac{{25}^{9x}}{{25}^6}$

Use the graph of the function $f\left(x\right)=2^{\frac{x}{2}}$ to solve the following exponential equation.

$2^{\frac{x}{2}}+5=9$

Use the graph of the function $f\left(x\right)=2^{2x}$ to solve the following exponential equation.

$2^{2x}-12=4$

Solve ${32}^{2x}\times 8=64$.

Solve $5^{3x}\times 25={125}^{2x}$.

If $\log 3^{x+4}=\log 729$ then the value of $x$ will be

If $5^{\log x}-3^{\log x-1}=3^{\log x+1}-5^{\log x-1}$, where the base of logarithm is ten, then find the value of $x.$

The value for the given  ${\log }_{\frac{9}{4}}\left(\frac{1}{2\sqrt{3}}\sqrt{6-\frac{1}{2\sqrt{3}}\sqrt{6-\frac{1}{2\sqrt{3}}\sqrt{6-\frac{1}{2\sqrt{3}}\dots ..\infty }}}\right)$

The equation $x^{\left[{\left({\log }_{3}x\right)}^2 -\frac{9}{2}{\log }_{3}x+5\right]}=3\sqrt{3}$ has

The given numbers of real solution of the equation $\sqrt{{\log }_{10}\left(-x\right)}={\log }_{10}\sqrt{x^2}$ is$.........$

If $a^x=b^y=c^z$ and $b^2=ac$, then find the value of $y$.

Evaluate the value of ${\log }_{81}3$ using the change of base formula.

If $f\left(x\right)={\log }_{2}x+{\log }_2\left(x^2-1\right)-{\log }_2\left(x+1\right)$ then

If $f\left(x\right)={\log }_{2}x+{\log }_2\left(x^2-1\right)-{\log }_2\left(x+1\right)$ then