3 . 2^{4x} + 2^{2x} – 10 = 0
adalah …
a. ^{2} log 5 – ^{2}log3 – ^{2} log3 . ^{2} log5
b. ^{2} log sqrt{5} – ^{2} log sqrt{3}
c. ^{2} log5 – ^{2} log sqrt{3}
d. ^{2} log sqrt{5} – ^{2} log3
e. log 25 – log 9
Nilai x yang memnuhi persamaan.
Jawaban Terkonfirmasi
Jawab
3 (2)⁴ˣ + (2)²ˣ -10 = 0
3 (2²ˣ)²+ (2²ˣ) – 10 = 0
misalkan (2²ˣ) = y , y > 0
3y² + y – 10 = 0
(3y – 5)(y + 2) =0
y = 5/3 atau y = – 2 ™
(2²ˣ) = 5/3
2x log 2= log 5 – log 3
2x= ²log 5 – ²log 3
x = 1/2 { ²log 5 – ²log 3)
x = ²log √5 – ²log √3