Question Number 207207 by hardmath last updated on 09/May/24
$$\mathrm{100}\:\mathrm{x}^{\boldsymbol{\mathrm{lg}}\:\boldsymbol{\mathrm{x}}} \:\:=\:\:\mathrm{x}^{\mathrm{3}} \\ $$$$\mathrm{Find}:\:\:\mathrm{x}\:=\:? \\ $$
Answered by mr W last updated on 09/May/24
$$\mathrm{100}={x}^{\mathrm{3}−\mathrm{log}\:{x}} \\ $$$$\mathrm{100}=\mathrm{10}^{\mathrm{2}} =\mathrm{10}^{\mathrm{3}−\mathrm{1}} =\mathrm{10}^{\mathrm{3}−\mathrm{log}\:\mathrm{10}} \\ $$$$\Rightarrow{x}=\mathrm{10} \\ $$