Question

Tolong dikerjain dgn cara​

Answer 1

Diketahui :

y = 2^x + 3

y = 18 - 9•2^(-x+2)

Ditanyakan :

AB = ?

y = y

2^x + 3 = 18 - 9•2(-x+2)

2^x = 15 - 9 • 2^-x • 4

2^x = 15 - 36/2^x

Misalkan

2^x = a

a = 15 - 36/a

a² = 15a - 36

a² - 15a + 36 = 0

(a -12)(a-3) = 0

a = 12 atau a = 3

• 2^x = 12

x1 = ²log12

• 2^x = 3

x2 = ²log 3

Subtitusi x1

• y = 2^x + 3

y = 2^(²log12) + 3

y1 = 15

Subtitusi x2

y = 2^x + 3

y = 2^(²log3) + 3

y2 = 6

AB = √[(6 - 15)² + ( ²log3 - ²log12)²]

AB = √[(81) + (4)]

AB = √ 85

Answer 2

Tipot

y = y

2^x + 3 = 18 - 9 . 2^-x + 2

2^x + 9 . 2^2 /2^x = 18 - 3

2^x + 36/2^x = 15

a + 36/a = 165

a² - 15a + 36 = 0

(a - 3)(a - 12) = 0

2^x = 3 → y = 2^x + 3 = 6

x = ²log 3 → A(²log 3, 6)

2^x = 12 → y = 12 + 3 = 15

x = ²log 12

Panjang garis AB

= √((²log 12 - ²log 3)² + (15 - 6)²)

= √((²log 4)² + 9²)

= √(4 + 81)

= √85 satuan