odpoveď:
# X = ln ((25 + -sqrt (609)) / (2sqrt (2))) / (LN4) #
vysvetlenie:
# 2 ^ (4x) -5 (2 ^ (2 x-1/2)) + 2 = 0 <=> #
# 2 ^ ((2x) ^ 2) -5 * 2 ^ (2x), farba (červená), (xx) 5 * 2 ^ (- 1/2) + 2 = 0 <=> #
# (2 ^ (2 x)) ^ 2- (25 / sqrt (2)), 2 ^ (2 x) + 2 = 0 <=> #
Teraz by mala byť ľahko viditeľná kvadratická rovnica.
Musíte ho vymeniť # 2 ^ (2 x) # s 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 ^ (2 x) = y = (25 / sqrt (2) + - sqrt (609/2)) / 2 #
Logické logy appylingu:
# 2xln2 = ln ((25 + -sqrt (609)) / (2sqrt (2))) #
# X = ln ((25 + -sqrt (609)) / (2sqrt (2))) / (2ln2) #
# X = ln ((25 + -sqrt (609)) / (2sqrt (2))) / (LN4) #
