Question

Jika x1 dan x2 memenuhi (4-log x) log x=log 1000 , maka x1x2 =…

Answer 1

(4-log x) log x = log 1000
4 log x - log²x = log 10³
4 log x - log²x = 3 log 10
4 log x - log²x = 3
misalkan log x = a
4a-a² = 3
a²-4a+3 = 0
(a-3)(a-1) = 0
a-3=0 atau a-1=0
a=3 atau a=1

untuk a=3
log x = 3
x = 10³
x = 1000
x₁ = 1000

untuk a=1
log x = 1
x = 10¹
x = 10
x₂ = 10

x₁x₂ = 1000 x 10 = 10000