Logarithms

If $x^2+y^2=7xy$ then, $\log \frac{1}{3}\left(x+y\right)=?$

Simplify:

$2^{16-{\log }_{2}1024}=?$

A circle has a radius of ${\log }_{10}\left({\mathrm{a}}^2\right)$ and a circumference of ${\log }_{10}\left({\mathrm{b}}^4\right)$. What is ${\log }_{\mathrm{a}}\mathrm{b}$?

If ${\log }_5{\log }_8\left(x^2-1\right)=0$, then a possible value of $\mathrm{x}$ is

The inequality ${\log }_2\frac{3x-1}{2-x}<1$ holds true for

Two distinct positive integers a and b are such that, ${\mathrm{a}}^{\mathrm{b}}={\mathrm{b}}^{\mathrm{a}}$ and ${\mathrm{a}}^{\frac{\mathrm{b}}{\mathrm{a}}}=2$, then the value of $(\mathrm{a}+\mathrm{b})$ is:

$\frac{1}{1+{\log }_a\left(bc\right)}+\frac{1}{1+{\log }_b\left(ca\right)}+\frac{1}{1+{\log }_c\left(ab\right)}$ is equal to _____.

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

The value of ${\left({\log }_{b}a \times {\log }_{c}b \times {\log }_{a}c\right)}^3$ is equal to _____

The simplified value of $2{\log }_{10}5+{\log }_{10}8-\frac{1}{2}{\log }_{10}4$ is _____

If ${\log }_{2}x+{\log }_{4}x+{\log }_{16}x=\frac{21}{4}$, these $x$ is equal to _____.

The value of ${\log }_2\left[{\log }_2\left\{{\log }_3\left({\log }_3{27}^3\right)\right\}\right]$ is equal to _____.

If $\log x+\log y=\log (x+y), y$ can be expressed as _____.

The value of $\log \frac{1}{3}$ to the base $9$ is ______.

The value of ${\log }_2{\log }_2{\log }_{2}16$ _____.

Given $\log 2=0.3010$ and $\log 3=0.4771$ the value of $\log 6$ is ______.

$\log 0.0625$ to the base $2$ is equal to _____.

$\log \left(\frac{1}{81}\right)$ to the base $9$ is equal to _____.

${\log }_{2\sqrt{3}}1728$ is equal to _____.

${\log }_{\sqrt{2}}64$ is equal to _____.