Question

3 la puterea 2x inmultit cu 9 la puterea x mai mic egal decat 81 la puterea 3-2x

Answer 1

Răspunsul - infinit 1

Answer 2

$\displaystyle 3^{2x} \cdot 9^x \leq 81^{3-2x} \\ 3^x(3^2 \cdot 3) \leq 81^{3-2x} \\ 3^x(9 \cdot 3) \leq 81^{3-2x} \\ 3^x \cdot 27 \leq 81^{3-2x} \\ 3^x \leq 81^{3-2x}:27 \\ 3^x \leq (3^4)^{3-2x}:3^3 \\ 3^x \leq 3^{12-8x}:3^3 \\ 3^x \leq 3^{12-8x-3} \\ 3^x \leq 3^{9-8x} \\ x \leq 9-8x \\ x+8x \leq 9 \\ 9x \leq 9 \\ x \leq \frac{9}{9} \\ x \leq 1$