Solve-for-real-numbers-5-x-4-1-x-25-x-16-1-x-2527-

Question Number 162102 by HongKing last updated on 26/Dec/21

Solve for real numbers :

5^{x} + 4^{\frac{1}{x}} + 25^{x} \cdot 16^{\frac{1}{x}} = 2527

Commented by mr W last updated on 26/Dec/21

s u c h t h a t 4^{\frac{1}{x}} i s i n t e g e r, x = 1 o r 2

t r y w i t h x = 1 :

5^{1} + 4^{1} + 25^{1} \times 16^{1} = 409

t r y w i t h x = 2 :

5^{2} + 4^{\frac{1}{2}} + 25^{2} \times 16^{\frac{1}{2}} = 2527 ✓

\Rightarrow x = 2 i s t h e r o o t

Commented by HongKing last updated on 28/Dec/21

thank you dear Sir