Question

Помогите решить уравнение $25^{(2x+6)} +16*4^{ (2x+4)}=20*10^{(2x+5)}$

Answer 1

$25^{(2x+6)} +16*4^{ (2x+4)}=20*10^{(2x+5)}$

$25^{(2x+6)} +4^{ (2x+6)} - 20*10^{(2x+5)} = 0$

$25^{(2x+6)} - 20*10^{(2x+5)} + {4}^{(2x + 6)} = 0$

$({5}^{(2x + 6)} - {2}^{(2x + 6)} ) {}^{2} = 0$

${5}^{(2x + 6)} = {2}^{(2x + 6)}$

${2.5}^{(2x + 6)} = 1$

$2.5 {}^{(2x + 6)} = (2.5) {}^{0}$

$2x + 6 = 0$

$x = - 3$