Logarithm question:)

Question

Log₃(3-x)+log₃(4-x)=1+2 log ₃2

i got the answer which is x=0, but I can’t figure out what the domain of it is. I got 3<x<4.

what I need to answer: what is the domain?

Answer 1

Domain: 3 - x > 0 and 4 - x> 0; x <3 and x < 4. Common x < 3.

(3 - x)(4 - x) = 3·2²; x² - 7x = 0, x(x - 7) = 0. From here x = 0 or x = 7. We regect 7 because it not in domain

Left only x = 0

Answer 2

You got one of the two values of x which satisfy the equation; the other value is 7.

Of what do you want the domain? Obviously th expression makes no sense for x greater than 3.