Question

2^(3x+7)+5^(3x+4)+2^(3x+5)-5^(3x+5)=0
помогите решить показательное уравнение

Answer 1

2^(3x+7)+5^(3x+4)+2^(3x+5)-5^(3x+5)=0
2^(3x+7)+2^(3x+5)=5^(3x+5)-5^(3x+4)
2^(3x+5) * (2^2 + 1) = 5^(3x+4) * (5^1 - 1)
2^(3x+5) * 5 = 5^(3x+4) * 4
2^(3x+3) * 2^2 * 5 = 5^(3x+3) * 5^1 * 4
2^(3x+3) = 5^(3x+3)
(5/2)^(3x+3) = 1
(5/2)^(3x+3) = (5/2)^0
3x+3=0
3x=-3
x=-1