Question

What values of x satisfy the following inequality :

${\log }_2\left(x\right)>{\log }_2\left(3\right)+{\log }_4\left(25\right)+{\log }_8\left(343\right)$ ?

Answer 1

Writing all the logarithms in base 2 gives

${\log }_2\left(x\right)>{\log }_2\left(3\right)+{\log }_2\left(5\right)+{\log }_2\left(7\right)$

${\log }_2\left(x\right)>{\log }_2\left(105\right)$

So, $x>105$

All x greater than 105 satisfy the original inequality.