Question

Nilai x yang memnuhi persamaan.
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

Answer 1

Verified answer

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 (tm)

(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