Question

Решите показательное неравенство 7^2x-9>7^3x-6

Answer 1

$7^{2x-9}\ \textgreater \ 7^{3x-6} \\ 2x-9\ \textgreater \ 3x-6 \\ -9+6\ \textgreater \ 3x-2x \\ x\ \textless \ -3 \\ x \in (-\infty;-3)$

Answer 2

${7}^{2x - 9} > {7}^{3x - 6} \\ 2x - 9 > 3x - 6 \\ 2x - 3x > - 6 + 9 \\ - x > 3 \\ x < - 3$

или

${7}^{2} x - 9 > {7}^{3} x - 6 \\ 49x - 9 > 343x - 6 \\ 49x - 343x > - 6 + 9 \\ - 294x > 3 \\ x < - \frac{1}{98}$