Question

ПОМОГИТЕ ПОЖАЛУЙСТА ПОКАЗАТЕЛЬНЫЕ УРАВНЕНИЕ​

Answer 1

a^mn = (a^m)^n

a^(m + n) = a^m*a^n

5^x + 5 = 3^(xlog(9) 5 + 2)

3^(xlog(9) 5 + 2) = 3^(xlog(3^2) 5) * 3^2 = 3^(xlog(3)√5)*9 = 9*3^(log(3)√5)^x = 9*√5^x

√5^x = t > 0

t^2 - 9t + 5 = 0

D = 81 - 20 = 61

t12 = (9 +- √61)/2

5^x = (9 +- √61)/2

x12 = log(5) (9 + - √61)/2

x1 + x2 = log(5) (9 - √61)/2 + log(5) (9 +  √61)/2 = log(5) ((9 +  √61)/2 * (9  - √61)/2 ) = log(5) ( 81 - 61)/4 = log(5) 20/4 = log(5) 5 = 1