Question

$3^{log_{3} (x+4)}=x^2+2x-26$

Answer 1

ОДЗ :

x + 4 > 0

x > - 4

$3^{log_{3}(x+4) }=x^{2}+2x-26\\x+4=x^{2}+2x-26\\x^{2}+2x-26-x-4=0\\x^{2} +x-30=0\\D=1^{2}-4*(-30)=1+120=121=11^{2}\\x_{1}=frac{-1+11}{2}=5\\x_{2}=frac{-1-11}{2}=-6$

Ответ : 5