Odgovor:
# x = (ln ((1 + sqrt (5)) / 2)) / (ln (3/2)) #
Pojasnilo:
Delite z # 4 ^ x # oblikovati kvadratno v # (3/2) ^ x #.
Uporaba # 6 ^ x / 4 ^ x = (6/4) ^ x = (3/2) ^ x in (9/4) ^ x = ((3/2) ^ 2) ^ x = ((3/2)) ^ x) ^ 2 #.
# ((3/2) ^ x) ^ 2- (3/2) ^ x-1 = 0 #
Torej,# (3/2) ^ x = (1 + -sqrt (1-4 * 1 * (- 1))) / 2 = (1 + -sqrt (5)) / 2 #
Za pozitivno rešitev:
# (3/2) ^ x = (1 + sqrt (5)) / 2 #
Uporaba logarythms:
#xln (3/2) = ln ((1 + sqrt (5)) / 2) #
# x = (ln ((1 + sqrt (5)) / 2)) / (ln (3/2)) = 1.18681439 …. #
