Log2 (2x+1)=2log2 3-log2 (x-4)

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First, use the properties of logarithms to simplify the equation:

Log2 (2x+1) = 2log2 3 - log2 (x-4)
Log2 (2x+1) = log2 (3^2) - log2 (x-4)^1
Log2 (2x+1) = log2 (9) - log2 (x-4)

Now, use the properties of logarithms to combine the logs on the right side:

Log2 (2x+1) = log2 (9/(x-4))

Since the bases of the logarithms are the same, we can set the arguments equal to each other:

2x + 1 = 9/(x-4)

Now, solve for x:

2x + 1 = 9/(x-4)
2x(x-4) + (x-4) = 9
2x^2 - 8x + x - 4 = 9
2x^2 - 7x - 13 = 0

Now, you can use the quadratic formula to solve for x:

x = (7 ± sqrt(7^2 - 42(-13))) / (2*2)
x = (7 ± sqrt(49 + 104)) / 4
x = (7 ± sqrt(153)) / 4

So, the solutions for x are:

x = (7 + sqrt(153)) / 4
x = (7 - sqrt(153)) / 4