Sagot:
# x = (ln ((1 + sqrt (5)) / 2)) / (ln (3/2)) #
Paliwanag:
Hatiin mo # 4 ^ x # upang bumuo ng isang parisukat sa # (3/2) ^ x #.
Gamitin # 6 ^ x / 4 ^ x = (6/4) ^ x = (3/2) ^ x at (9/4) ^ x = ((3/2) ^ 2) ^ x = ((3/2) ^ x) ^ 2 #.
# ((3/2) ^ x) ^ 2- (3/2) ^ x-1 = 0 #
Kaya,# (3/2) ^ x = (1 + -sqrt (1-4 * 1 * (- 1))) / 2 = (1 + -sqrt (5)) / 2 #
Para sa positibong solusyon:
# (3/2) ^ x = (1 + sqrt (5)) / 2 #
Paglalapat ng logarythms:
#xln (3/2) = ln ((1 + sqrt (5)) / 2) #
# x = (ln ((1 + sqrt (5)) / 2)) / (ln (3/2)) = 1.18681439 …. #
