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

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

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

$$\frac{7^{\mathit{x}}}{1+7^{\mathit{x}}}=\frac{3}{7};\frac{{2401}^{\mathit{x}}}{1+{2401}^{\mathit{x}}}=?$$$$3+3\cdot 7^x=7\cdot 7^x$$$$\frac{3}{7^x}+3=7$$$$\frac{3}{7^x}=4$$$$7^x=\frac{3}{4}$$$$\frac{{2401}^{\mathbf{x}}}{1+{2401}^{\mathbf{x}}}=\frac{{\left(7^x\right)}^4}{1+{\left(7^x\right)}^4}=\frac{{\left(\frac{3}{4}\right)}^4}{1+{\left(\frac{3}{4}\right)}^4}$$$$=\frac{3^4}{3^4+4^4}$$

Commented by Shrinava last updated on 25/Feb/23

$$thankyoudearprofessor$$

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