Prosimo, rešite q 5?

Odgovor:

Glej spodaj.

Pojasnilo:

Imamo, #barva (bela) (xxx) a ^ (2x - 3) * b ^ (2x) = a ^ (6-x) * b ^ (5x) #

#rArr a ^ (2x - 3) / a ^ (6-x) = b ^ (5x) / b ^ (2x) #

Samo prenesite # a # in # b # na svojih straneh.

#rArr a ^ ((2x - 3) - (6 - x)) = b ^ (5x - 2x) # Kot # a ^ (m-n) = a ^ m / a ^ n #

#rArr a ^ (2x - 3 - 6 + x) = b ^ (3x) #

#rArr a ^ (3x - 9) = b ^ (3x) #

#rArr (a (x - 3)) ^ 3 = (b ^ x) ^ 3 # Kot, # (x ^ m) ^ n = x ^ (mn) #

#rArr a ^ (x - 3) = b ^ x #

#rArr a ^ x / a ^ 3 = b ^ x # Kot # a ^ (m-n) = a ^ m / a ^ n #

#rArr a ^ x / b ^ x = a ^ 3 # Ponovno prenos

#rArr (a / b) ^ x = a ^ 3 # Kot # (a / b) ^ m = a ^ m / b ^ m #

#rArr log (a / b) ^ x = prijavite ^ 3 # Vzamem # log # na obeh straneh

#rArr x log (a / b) = 3 log a # Kot #log a ^ x = x prijavite #

#rArr 3 log a = x log (a / b) #

Zato je dokazano.