SOLUTION: Calcalate the value for z which 2log3(Y)-log3(y+4)= 2

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Question 139914: Calcalate the value for z which
2log3(Y)-log3(y+4)= 2
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
2log%283%2CY%29-log%283%2C%28y%2B4%29%29=+2
log%283%2CY%5E2%29-log%283%2C%28y%2B4%29%29=+2
log%283%2C%28Y%5E2%29%2F%28y%2B4%29%29=+2
By basic definition of logarithms,
3%5E2+=+%28y%5E2%29%2F%28y%2B4%29+
9=%28y%5E2%29%2F%28y%2B4%29+

Multiply both sides of the equation by (y+4):
9%28y%2B4%29+=+y%5E2
9y%2B36=y%5E2
y%5E2+-+9y+-36=0

It's a quadratic equation, but, lo and behold, IT FACTORS!! Life is GOOD, isn't it?? (Well, sometimes!!)

y%5E2+-+9y+-36=0
%28y-12%29%28y%2B3%29=0
y=12 or y=-3

Reject the negative answer, since you can't have a log of a negative.
y=12

Please see my entire chapter on logarithms. Go to my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take the second link, which is "Basic, Intermediate, or College Algebra: One Step at a Time." Look for "College Algebra", "Chapter 4 Logarithms", "Section 4.04"! This is an explanation on LOGARITHMS that was written for people who have a hard time understanding math! I think if you have a hard time with logarithms, you will like this chapter!!!

R^2