Question

4^х=3*49^х-2*14^х поможіть ​

Answer 1

$4 {}^{x} = 3 \times 49 {}^{x} - 2 \times 14 {}^{x}$

$4^{x} - 3 \times 49^{x} + 2 + 14 ^{x} = 0$

${2}^{2x} - 3 + {7}^{2x} \times (2 \times 7) ^{x} = 0$

${2}^{2x} - 3 + {7}^{2x} + 2 \times 2 ^{x} \times 7 {}^{x} = 0$

$( \frac{2}{7} ) {}^{2x} - 3 + 2 \times ( \frac{2}{7} )^{x} = 0$

$(( \frac{2}{7} ) {}^{x} ) {}^{2} - 3 + 2 \times (\frac{2}{7} )^{x} = 0$

$t {}^{2} - 3 + 2t = 0$

$t = - 3 \\ t = 1$

$x = 0$