Question Number 187442 by Shrinava last updated on 17/Feb/23
$$\mathrm{If}\:\:\:\:\:\frac{\mathrm{7}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}\:+\:\mathrm{7}^{\boldsymbol{\mathrm{x}}} }\:\:=\:\:\frac{\mathrm{3}}{\mathrm{7}}\:\:\:\:\:\mathrm{find}\:\:\:\:\frac{\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}\:+\:\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }\:\:=\:\:? \\ $$
Answered by Rasheed.Sindhi last updated on 17/Feb/23
$$\frac{\mathrm{7}^{\boldsymbol{{x}}} }{\mathrm{1}\:+\:\mathrm{7}^{\boldsymbol{{x}}} }\:\:=\:\:\frac{\mathrm{3}}{\mathrm{7}}\:\:\:\:\:;\:\:\:\:\:\:\frac{\mathrm{2401}^{\boldsymbol{{x}}} }{\mathrm{1}\:+\:\mathrm{2401}^{\boldsymbol{{x}}} }\:\:=\:\:? \\ $$$$\mathrm{3}+\mathrm{3}\centerdot\mathrm{7}^{{x}} =\mathrm{7}\centerdot\mathrm{7}^{{x}} \\ $$$$\frac{\mathrm{3}}{\mathrm{7}^{{x}} }+\mathrm{3}=\mathrm{7} \\ $$$$\frac{\mathrm{3}}{\mathrm{7}^{{x}} }=\mathrm{4} \\ $$$$\mathrm{7}^{{x}} =\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\frac{\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}\:+\:\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }=\frac{\left(\mathrm{7}^{{x}} \right)^{\mathrm{4}} }{\mathrm{1}+\left(\mathrm{7}^{{x}} \right)^{\mathrm{4}} }=\frac{\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{4}} }{\mathrm{1}+\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{4}} } \\ $$$$=\frac{\mathrm{3}^{\mathrm{4}} }{\mathrm{3}^{\mathrm{4}} +\mathrm{4}^{\mathrm{4}} } \\ $$
Commented by Shrinava last updated on 25/Feb/23
$${thank}\:{you}\:{dear}\:{professor} \\ $$