Question

Wo schneiden sich f und g?

f(x)=1/3*3^x 

g(x)=1/27*9^x

Wie berechne ich das?

Answer 1

1/3*3^x=1/27*9^x  |*27

9*3^x=9^x  |/3^x

9=(9/3)^x

9=3^x

3^2=3^x

Exponentenvergleich

x=2

Answer 2

1/3*3^x = 1/27*9^x

3^(x-1)= 3^(2x-3)

x-1 = 2x-3

x=2

Answer 3

1/3 * 3^x = 1/27 * 9^x

3^{-1} * 3^x = 3^{-3} * (3^2)^x

3^{x - 1} = 3^{-3} * 3^{2·x}

3^{x - 1} = 3^{2·x - 3}

Exponentenvergleich

x - 1 = 2·x - 3

- 1 = x - 3

2 = x