Jawapan:
# x = ln ((25 + -sqrt (609)) / (2sqrt (2))) / (ln4) #
Penjelasan:
# 2 ^ (4x) -5 (2 ^ (2x-1/2)) + 2 = 0 <=> #
# 2 ^ (2x) ^ 2) -5 * 2 ^ (2x) warna (merah) (xx) 5 * 2 ^ (- 1/2) + 2 =
# (2 ^ (2x)) ^ 2- (25 / sqrt (2)) 2 ^ (2x) + 2 = 0 <=> #
Sekarang persamaan kuadratik harus mudah dilihat.
Anda perlu mengganti # 2 ^ (2x) # dengan y.
# <=> y ^ 2 (25 / (2)) y + 2 = 0 #
# y = (25 / sqrt (2) + - sqrt (625 / 2-2 * 2 * 2)) / 2 #
# y = (25 / sqrt (2) + - sqrt (609/2)) / 2 #
# 2 ^ (2x) = y = (25 / sqrt (2) + - sqrt (609/2)) / 2 #
Logaritma yang menarik:
# 2xln2 = ln ((25 + -sqrt (609)) / (2sqrt (2))) #
# x = ln ((25 + -sqrt (609)) / (2sqrt (2))) / (2ln2) #
# x = ln ((25 + -sqrt (609)) / (2sqrt (2))) / (ln4) #
