Exponents and Logarithms

Find the value of ${\left(897\right)}^2$.

If $3^{x+3}+7=250$, then the value of $x$ is _____

If $x={\log }_{24}12; y={\log }_{36}24; z={\log }_{48}36;$
then $xyz+1=?$

Which of the following in the largest number?

$2^{\frac{1}{2}}, 3^{\frac{1}{3}}, 6^{\frac{1}{6}}, {12}^{\frac{1}{12}}$

$\frac{1}{{\log }_a b}\times \frac{1}{{\log }_{b }c}\times \frac{1}{{\log }_c a}$ is equal to __________.

If $2^{\mathrm{m}}-2^{\mathrm{m}-1}-4=0$ then find the value of ${\mathrm{m}}^{\mathrm{m}}$.

If $x^n+a^n$ is divisible by $x + a$Only, Then $n$is what$?$ ?

Which statement is true

What is the value of 'P',$4^{2p}=\frac{1}{6}$?

Which of the two is greater $2^{300}$or $3^{200}$?

The expression ${\left(27+\sqrt{756}\right)}^{\frac{1}{3}}+{\left(27-\sqrt{756}\right)}^{\frac{1}{3}}$ is equal to _______?

$\log (1+2+3)$ is exactly equal to

If $x=3^{\frac{1}{3}}+3^{-\frac{1}{3}}$, then $3x^3-9x$ is _____

The value of ${\left(\frac{8}{27}\right)}^{\frac{-1}{3}}\times {\left(\frac{32}{243}\right)}^{\frac{-1}{5}}$ is ______.

Solving equation ${\left(1+x\right)}^{\frac{2}{3}}+{\left(1-x\right)}^{\frac{2}{3}}=4{\left(1-x^2\right)}^{\frac{1}{3}}$ are, values of $x$

What should come in the place of ($?$) for the expression given below?

${\log }_2\left(4\right)-\frac{{\log }_3\left(9\right)}{{\log }_4\left(16\right)}+\frac{{\log }_5\left(25\right)}{{\log }_6\left(36\right)}=?$

What should come in the place of ($?$) for the expression given below?

$\frac{{\log }_{10}\left(100\right)}{{\log }_5\left(25\right)}+\frac{{\log }_{10}\left(10\right)}{{\log }_5\left(5\right)}+\frac{{\log }_{10}\left(1000\right)}{{\log }_5\left(125\right)}=?$

If $3^{\mathrm{x}}=115+2^{\mathrm{y}}$ and $3^{\mathrm{x}-4}+2^{\mathrm{y}-5}=7,$ find $\mathrm{x}+\mathrm{y}$

If $\left(250\sqrt{2}{\mathrm{x}}^3+24\sqrt{3}{\mathrm{y}}^3\right)÷(5\sqrt{2}\mathrm{x}+2\sqrt{3}\mathrm{y})=\left({\mathrm{Ax}}^2+{\mathrm{By}}^2-\mathrm{c}\sqrt{6}\mathrm{xy}\right),$ then the value of $\left(\frac{\mathrm{A}}{10}+\frac{{\mathrm{B}}^2}{8}+\mathrm{C}\right)$ is

Find the value of $\frac{{\log }_{3}16}{{\log }_{9}8\times {\log }_{4}10} :$