Question Number 172151 by Giantyusuf last updated on 23/Jun/22
$$\mathrm{3}^{{x}} =\mathrm{10}−{log}_{\mathrm{2}} {x} \\ $$$${find}\:{x} \\ $$
Answered by aleks041103 last updated on 23/Jun/22
$$\mathrm{3}^{{x}} \:{is}\:{monotounously}\:{increasing}. \\ $$$$\mathrm{10}−{log}_{\mathrm{2}} {x}\:{is}\:{monotounously}\:{decreasing}. \\ $$$$\Rightarrow\mathrm{3}^{{x}} =\mathrm{10}−{log}_{\mathrm{2}} {x}\:{has}\:{at}\:{most}\:\mathrm{1}\:{soln}. \\ $$$${by}\:{inspection}\:{x}=\mathrm{2}\:{is}\:{a}\:{solution} \\ $$$$\Rightarrow{The}\:{only}\:{solution}\:{is}\:{x}=\mathrm{2}. \\ $$
Answered by Mikenice last updated on 23/Jun/22
