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

Question 458397: Can anyone please help me with this problem?

Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
2log y+2 = logy+2-log12
-----
2log(y) + 2 = log(y)+2 - log(12)
log(y) = -log(12)
y = -12
----
But y cannot negative as log(-12) is meaningless.
================
Conclusion: No solution
=====================
Cheers,
Stan H.
=====================
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
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:
.

.
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:
.

.
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:
.

.
From here on out it's just a "normal" algebraic exercise. First square the left side of the equation:
.

.
Next get rid of the denominator on the right side by multiplying both sides of the equation by 12 to get:
.

.
Subtract 2 from both sides to eliminate the 2 on the right side:
.

.
And eliminate the y on the right side by subtracting y from both sides:
.

.
This is an equation in the standard quadratic form

.
and so the quadratic formula can be used as follows:
.

.

.

.

.
Since the square root of 1 is 1, this leads to the two answers:
.
which simplifies to
.
and
.
which simplifies to
'
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.
RELATED QUESTIONS
Please help me with the following problem: 2log(y+2)=log(y+2)-log12 What I tried - (answered by Nate)
can anyone help me with this factoring algebra problem... (answered by RAY100)
can anyone help me with this problem in factoring... (answered by rfer)
Can anyone help me with this problem? Thanks! Factor.Check by multiplying... (answered by jim_thompson5910)
Can anyone please help me with this problem? FInd the value of y: 3x-2y=-7... (answered by gonzo)
Can anyone help me this with complex fraction please?... (answered by Fombitz)
Can ANYONE help me with this problem? No one seems to know the foci of this equation.... (answered by jim_thompson5910)
Can someone please help me with this problem: y^2 + 5y - 14 / y^2 + 3y -... (answered by jim_thompson5910)
Can u please solve this x for me... (answered by Alan3354,MathTherapy)