Question Number 75840 by gugum last updated on 18/Dec/19 | ||
$$\mathrm{If}\:\:{x}^{\mathrm{200}} \:<\:\mathrm{3}^{\mathrm{300}} \:,\:\mathrm{then}\:\mathrm{greatest}\:\mathrm{possible} \\ $$ $$\mathrm{integral}\:\mathrm{value}\:\mathrm{of}\:\:\:{x}\:\:\mathrm{is}\:\_\_\_\_\_. \\ $$ | ||
Answered by mr W last updated on 19/Dec/19 | ||
$${x}^{\mathrm{200}} <\mathrm{3}^{\mathrm{300}} \\ $$ $$\left({x}^{\mathrm{2}} \right)^{\mathrm{100}} <\left(\mathrm{3}^{\mathrm{3}} \right)^{\mathrm{100}} \\ $$ $${x}^{\mathrm{2}} <\mathrm{3}^{\mathrm{3}} =\mathrm{27} \\ $$ $${x}<\sqrt{\mathrm{27}} \\ $$ $${x}\leqslant\mathrm{5} \\ $$ $$\Rightarrow{x}_{{max}} =\mathrm{5} \\ $$ | ||