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Question Number 187442 by Shrinava last updated on 17/Feb/23

If (7^x /(1 + 7^x )) = (3/7) find ((2401^x )/(1 + 2401^x )) = ?

$$\mathrm{If}\:\:\:\:\:\frac{\mathrm{7}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}\:+\:\mathrm{7}^{\boldsymbol{\mathrm{x}}} }\:\:=\:\:\frac{\mathrm{3}}{\mathrm{7}}\:\:\:\:\:\mathrm{find}\:\:\:\:\frac{\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}\:+\:\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }\:\:=\:\:? \\ $$

Answered by Rasheed.Sindhi last updated on 17/Feb/23

(7^x /(1 + 7^x )) = (3/7) ; ((2401^x )/(1 + 2401^x )) = ? 3+3∙7^x =7∙7^x (3/7^x )+3=7 (3/7^x )=4 7^x =(3/4) ((2401^x )/(1 + 2401^x ))=(((7^x )^4 )/(1+(7^x )^4 ))=((((3/4))^4 )/(1+((3/4))^4 )) =(3^4 /(3^4 +4^4 ))

$$\frac{\mathrm{7}^{\boldsymbol{{x}}} }{\mathrm{1}\:+\:\mathrm{7}^{\boldsymbol{{x}}} }\:\:=\:\:\frac{\mathrm{3}}{\mathrm{7}}\:\:\:\:\:;\:\:\:\:\:\:\frac{\mathrm{2401}^{\boldsymbol{{x}}} }{\mathrm{1}\:+\:\mathrm{2401}^{\boldsymbol{{x}}} }\:\:=\:\:? \\ $$$$\mathrm{3}+\mathrm{3}\centerdot\mathrm{7}^{{x}} =\mathrm{7}\centerdot\mathrm{7}^{{x}} \\ $$$$\frac{\mathrm{3}}{\mathrm{7}^{{x}} }+\mathrm{3}=\mathrm{7} \\ $$$$\frac{\mathrm{3}}{\mathrm{7}^{{x}} }=\mathrm{4} \\ $$$$\mathrm{7}^{{x}} =\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\frac{\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }{\mathrm{1}\:+\:\mathrm{2401}^{\boldsymbol{\mathrm{x}}} }=\frac{\left(\mathrm{7}^{{x}} \right)^{\mathrm{4}} }{\mathrm{1}+\left(\mathrm{7}^{{x}} \right)^{\mathrm{4}} }=\frac{\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{4}} }{\mathrm{1}+\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{4}} } \\ $$$$=\frac{\mathrm{3}^{\mathrm{4}} }{\mathrm{3}^{\mathrm{4}} +\mathrm{4}^{\mathrm{4}} } \\ $$

Commented by Shrinava last updated on 25/Feb/23

thank you dear professor

$${thank}\:{you}\:{dear}\:{professor} \\ $$

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