Question

Express y as a function of x. What is the domain? a) log 3 + log y = log (x+2) - log x

Answer 1

log a + log b = log(ab)

Answer 2

i strongly suggest you put everything as one log first

Answer 3

and log a - log b = log (a/b)

Answer 4

log(y)=log(x+2)-log(x)-log(3)
log(y)=log(x+2)-(log(x)+log(3))
log(y)=log(x+2)-(log3x)
log(y)=log((x+2)/3x)
exponentiating both sides
y = (x+2)/3x
domain is all real x except x =0
i think im wrong

Answer 5

log (3y) = log (\(\cfrac{x+2}{x}\))

Answer 6

3y = \(\cfrac{x+2}{x}\)

y = \(\cfrac{x+2}{3x}\)

Answer 7

Extremity you're close the answer is: {x< -2 or x > 0}

Answer 8

I'm confused about the domain though..

Answer 9

oh whoops, dangerous
(x+2)/3x > 0 , since log has to always be positive
that means
(x+2)3x>0
(x+2)x>0
graph a parabola and you see that
x<-2 and x>0
point is, when you make y the subject, you remove a fundamental analysis on the equation. that is, the presence of the log, and so the domain is what it is