Question

Jika 4*3 log a + 3*3 log b = 6 dan 3 log b - 2*3 log a = -8, maka ab^2 adalah...

Answer 1

Verified answer

4 . ³log a + 3 . ³log b = 6
³log b - 2 . ³log a = - 8
Misal
³log a = x
³log b = y

4x + 3y = 6 ... (1)

-2x + y = -8
y = -8 + 2x ... (2)

»Substitusi (2) ke (1)
4x + 3(-8 + 2x) = 6
4x - 24 + 6x = 6
10x = 30
x = 3

» Substitusi x = 3 ke (2)
y = -8 + 2(3)
y = -2

³log a = 3
³log a = ³log 27
a = 27

³log b = -2
³log b = ³log(1/9)
b = 1/9

maka,
ab²
= 27 x (1/9)²
= 27 x 1/81
= 1/3