Question

Diberikan y=ax^b +2. Jika x=3, maka y=7 dan jika x=9, maka y=52. Tentukan nilai (a.b) dan (a+b).

Answer 1

Y = ax^b + 2
x = 3 => y = 7
7 = a(3)^b + 2
=> 5 = a . 3^b
=> 3^b = 5/a

x = 9 => y = 52
52 = a . 9^b + 2
=> 52 - 2 = a . (3^2b)
=> 50 = a (3^b)^2
=> 50 = a (5/a)^2
=> 50 = a . 25/a^2
=> 50 = 25/a
=> a = 25/50 = 1/2

3^b = 5/a
=> 3^b = 5/(1/2)
=> 3^b = 10
=> b = 3log10

ab = 1/2 . 3log10 = 3log10^(1/2) = 3log√10
a + b = 1/2 + 3log10 = 3log3^(1/2) + 3log10 = 3log√3 + 3log10 = 3log10√3