If-7-x-1-7-x-3-7-find-2401-x-1-2401-x-

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

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

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

\frac{7^{x}}{1 + 7^{x}} = \frac{3}{7}; \frac{2401^{x}}{1 + 2401^{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^{x}}{1 + 2401^{x}} = \frac{{(7^{x})}^{4}}{1 + {(7^{x})}^{4}} = \frac{{(\frac{3}{4})}^{4}}{1 + {(\frac{3}{4})}^{4}}

= \frac{3^{4}}{3^{4} + 4^{4}}

Commented by Shrinava last updated on 25/Feb/23

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