SOLUTION: Can anyone please help me with this problem? {{{2log y+2=logy+2-log12}}}

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Question 458397: Can anyone please help me with this problem?
2log+y%2B2=logy%2B2-log12
Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2log y+2 = logy+2-log12
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2log(y) + 2 = log(y)+2 - log(12)
log(y) = -log(12)
y = -12
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But y cannot negative as log(-12) is meaningless.
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Conclusion: No solution
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Cheers,
Stan H.
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Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
2log%28y%2B2%29=log%28y%2B2%29-log12
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On the right side of the equation, the difference of the logs of two quantities is equal to the log of the division of the two quantities. The quantity having the negative signed log becomes the denominator and the quantity having the positive log is the numerator. So the right side becomes as shown below:
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2log%28y%2B2%29+=+log%28%28y%2B2%29%2F12%29
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On the left side the multiplier of a log (in this problem it is 2) is equivalent to the exponent of the quantity for which the log is being taken. So 2 can be converted to the exponent on the left side as indicated:
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log%28%28y%2B2%29%5E2%29+=+log%28%28y%2B2%29%2F12%29
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Now notice that on each side of the equation there is a single log operator. Therefore, in order for this equation to be true, the two quantities on which the log function operates must be equal. So we can say:
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%28y%2B2%29%5E2+=+%28y%2B2%29%2F12
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From here on out it's just a "normal" algebraic exercise. First square the left side of the equation:
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y%5E2+%2B+4y+%2B+4+=+%28y%2B2%29%2F12
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Next get rid of the denominator on the right side by multiplying both sides of the equation by 12 to get:
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12y%5E2+%2B+48y+%2B+48+=+y+%2B+2
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Subtract 2 from both sides to eliminate the 2 on the right side:
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12y%5E2+%2B+48y+%2B+46+=+y
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And eliminate the y on the right side by subtracting y from both sides:
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12y%5E2+%2B+47y+%2B+46+=+0
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This is an equation in the standard quadratic form
ay%5E2+%2B+by+%2B+c+=+0
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and so the quadratic formula can be used as follows:
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y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
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y+=+%28-47+%2B-+sqrt%28+47%5E2-4%2A12%2A46+%29%29%2F%282%2A12%29
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y+=+%28-47+%2B-+sqrt%28+2209-2208+%29%29%2F%2824%29
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y+=+%28-47+%2B-+sqrt+%281%29%29%2F24
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Since the square root of 1 is 1, this leads to the two answers:
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y+=+-46%2F24 which simplifies to y+=+-23%2F12
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and
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y+=+-48%2F24 which simplifies to y+=+-2
'
Hope this helps you to understand the problem. Please check my work to ensure that I interpreted your original problem correctly and also to ensure that I haven't made a dumb math mistake somewhere that would change the answer.