Mangyaring lutasin ang q 5?

Sagot:

Tingnan sa ibaba.

Paliwanag:

Meron kami, #color (white) (xxx) a ^ (2x - 3) * b ^ (2x) = a ^ (6-x) * b ^ (5x) #

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

Palitan lang ang # a # at # b # sa kanilang mga panig.

#rArr a ^ ((2x - 3) - (6 - x)) = b ^ (5x - 2x) # As # 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 # Bilang, # (x ^ m) ^ n = x ^ (mn) #

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

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

#rArr a ^ x / b ^ x = a ^ 3 # Naglilipat muli

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

#rArr log (a / b) ^ x = mag-log a ^ 3 # Pagkuha # mag-log # sa magkabilang panig

#rArr x log (a / b) = 3 mag-log a # As #log a ^ x = x log a #

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

Kaya napatunayan na.