SOLUTION: Express y as a function of x. What is the domain? a) log(base 2)xy = 3log(base 2)x b) log(base 5)y = 2log(base 5)x+1 + log(base 5)x-1 b) log(base 3)y-3 = 1 + 2log(base 3) Can

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Question 744924: Express y as a function of x. What is the domain?
a) log(base 2)xy = 3log(base 2)x
b) log(base 5)y = 2log(base 5)x+1 + log(base 5)x-1
b) log(base 3)y-3 = 1 + 2log(base 3)
Can you please help me out? Thanks so much in advance:)
Can you also show all the steps because it would help me understand :)
Found 2 solutions by stanbon, rothauserc:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Express y as a function of x. What is the domain?
a) log(base 2)xy = 3log(base 2)x
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log2(x)+log2(y) = log2(3^x)
log2(y) = log2(3^x)-log2(x)
log2(y) = log2[3^x/x]
y = 3^x*x
Domain: x > 0
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b) log(base 5)y = 2log(base 5)x+1 + log(base 5)x-1
log5(y) = log5[(x+1)^2 * (x-1)]
y = (x+1)^2*(x-1)
Domain: x > 1
============================================
b) log(base 3)y-3 = 1 + 2log(base 3)?
log3(y-3) = 1 + log3(?^2)
Domain: x > 3
==========================================
Note: The ? is there because your post is missing something.
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Cheers,
Stan H.

Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
The problem states:
Express y as a function of x. What is the domain?
a) log(base 2)xy = 3log(base 2)x
b) log(base 5)y = 2log(base 5)x+1 + log(base 5)x-1
b) log(base 3)y-3 = 1 + 2log(base 3)
First notice that each problem has the same log base on both sides of =
a) we can divide both sides of = by log(base 2) which gives us
xy = 3x and y = 3 (all rational numbers)
b) divide both sides of = by log(base 5) and we get
y = 2x+2 + x-1
y = x+1 (domain is all rational numbers)
c) divide both sides of = by log(base 3) and we get
y-3 = 1 + 2
y = 6 (domain is all rational numbers)