Решите уравнение (8/27)^(х+1)=(16/81)^(х+1)

Question

Решите уравнение (8/27)^(х+1)=(16/81)^(х+1)

Answer 1

8/27 =(2/3)^3 и 16/81 =(2/3)^4, тогда:

((2/3)^3)^(x +1) =((2/3)^4)^(x +1)

3(x +1) =4(x +1)

3(x +1) - 4(x +1) =0

(x +1)(3 -4) =0

-(x +1) =0

-x -1 =0

-x =1

x = -1