halo
jika xy = 50 dan ²log x - ²log y = 1
maka x - y ....![]()
jika xy = 50 dan ²log x - ²log y = 1
maka x - y ....
Math_
xy = 50 ...(1)
²log x - ²log y = 1 ...(2)
- Ubah bentuk pers. (1)
xy = 50
y = 50/x ...(3)
- Substitusi ke pers. (2)
²log x - ²log y = 1
²log x - ²log (50/x) = 1
²log x - ( ²log 50 - ²log x ) = 1
²log x - ²log 50 + ²log x = 1
2 ²log x - ²log 50
²log x² - ²log 50 = 1
²log ( x²/50 ) = 1
( x²/50 ) = 2¹
x² = ( 50 × 2¹ )
x² = 100
x = √100
x = 10
- Substitusi nilai x ke pers (3)
y = 50/x
y = 50/10
y = 5
- Nilai x - y
x - y
= 10 - 5
= 5
krksi
xy = 50 .... pers 1
²log x - ²log y = 1
²log x/y = 1
x/y = 2¹
x/y = 2
x = 2y .... pers 2
.
substitusi pers 2 ke pers 1
xy = 50
(2y)y = 50
2y² = 50
y² = 50/2
y² = 25
y = √25
y = 5
.
Menentukan x
xy = 50
x = 50/y
x = 50/5
x = 10
.
Maka,
x - y
= 10 - 5
= 5
[answer.2.content]
