First, use the properties of logarithms to simplify the equation:
Log2 (2x+1) = 2log2 3 - log2 (x-4Log2 (2x+1) = log2 (3^2) - log2 (x-4)^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-42x(x-4) + (x-4) = 2x^2 - 8x + x - 4 = 2x^2 - 7x - 13 = 0
Now, you can use the quadratic formula to solve for x:
x = (7 ± sqrt(7^2 - 42(-13))) / (2*2x = (7 ± sqrt(49 + 104)) / x = (7 ± sqrt(153)) / 4
So, the solutions for x are:
x = (7 + sqrt(153)) / x = (7 - sqrt(153)) / 4
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)^
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) =
2x^2 - 8x + x - 4 =
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)) /
x = (7 ± sqrt(153)) / 4
So, the solutions for x are:
x = (7 + sqrt(153)) /
x = (7 - sqrt(153)) / 4