Logarithm

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

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

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

If $\mathrm{x}>\mathrm{y}$ and $\mathrm{y}>1$, then the value of the expression ${\log }_x\left(\frac{\mathrm{x}}{\mathrm{y}}\right)+{\log }_{\mathrm{y}}\left(\frac{\mathrm{y}}{\mathrm{x}}\right)$ can never be:

Find the value of $\mathrm{x}$, if ${\log }_{\sqrt{2}}\left[{\log }_{\sqrt{2}}\left({\log }_{\sqrt{3}}\left(\mathrm{logx}\right)\right)\right]=2$

If $\mathrm{x}$ and $\mathrm{y}$ are positive integers for which $2^{\mathrm{x}}{3}^{\mathrm{y}}=1296$, what is the value of $\mathrm{x}+\mathrm{y}$ ?

Let $\mathrm{U}=2\times {2004}^{2005}, \mathrm{V}={2004}^{2005}, \mathrm{W}=2003$ $\times {2004}^{2004}, \mathrm{X}=2\times {2004}^{2004}, \mathrm{Y}={2004}^{2004}$, and $\mathrm{Z}$ $={2004}^{2003}$. Which of the following is the largest?

If$\log \left({\mathrm{xy}}^3\right)=1$ and $\log \left({\mathrm{x}}^2\mathrm{y}\right)=1$, what is $\log \left(\mathrm{xy}\right)$ ?

The value of ${\left({\log }_{3}30\right)}^{-1}+{\left({\log }_{4}900\right)}^{-1}+{\left({\log }_{5}30\right)}^{-1}$ is

The inequality ${\log }_a\left\{f\right(x\left)\right\}<{\log }_a\left\{g\right(x\left)\right\}$ implies that

If $\mathrm{h}\left(\mathrm{x}\right)=\frac{{\mathrm{e}}^{2\mathrm{x}}}{{\mathrm{e}}^{2\mathrm{x}}+\mathrm{e}}$, then the value of $\mathrm{h}\left(\frac{1}{4}\right)+\mathrm{h}\left(\frac{3}{4}\right)$ will be:

If $x={\log }_{a}bc; y={\log }_{b}ca; z={\log }_{c}ab$ then the value of $xyz-x-y-z$ is___

If $a^3+b^3=0$ then the value of $\log \left(a+b\right)-\frac{1}{2}\left(\log a+\log b+\log 3\right)$ is equal to____

$\frac{1}{a^{{\log }_{b}a}}$ has a value of______

The sum of the series ${\log }_{a}b+{\log }_{a^2}{b}^2+{\log }_{a^3}{b}^3+.....{\log }_{a^n}{b}^n$ is given by_______.

The value of $\log \frac{a^2}{bc}+\log \frac{b^2}{ca}+\log \frac{c^2}{ab}$ is _____.

The value of ${\left(bc\right)}^{\log \raisebox{1ex}{$b$}\!\left/ \!\raisebox{-1ex}{$c$}\right.}·{\left(ca\right)}^{\log \raisebox{1ex}{$c$}\!\left/ \!\raisebox{-1ex}{$a$}\right.}·{\left(ab\right)}^{\log \raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$b$}\right.}$ is _____.

The value of is $a^{\log \raisebox{1ex}{$b$}\!\left/ \!\raisebox{-1ex}{$c$}\right.}·b^{\log \raisebox{1ex}{$c$}\!\left/ \!\raisebox{-1ex}{$a$}\right.}·c^{\log \raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$b$}\right.}$

${\log }_b\left(a^{\frac{1}{2}}\right)·{\log }_c\left(b^3\right)·{\log }_a\left(c^{\frac{2}{3}}\right)$ is equal to _____.

${\log }_b\left(a\right).{\log }_c\left(b\right).{\log }_a\left(c\right)$ is equal to _____.