First, we need to use the properties of logarithms to combine the terms on the left side of the equation. We know that log(a) - log(b) = log(a/b) and log(a) + log(b) = log(ab).
log2 (6-x^2) = log2 5x
log2((6-x^2)/5x) = 0
Now, simplify the expression inside the logarithm:
First, we need to use the properties of logarithms to combine the terms on the left side of the equation. We know that log(a) - log(b) = log(a/b) and log(a) + log(b) = log(ab).
log2 (6-x^2) = log2 5x
log2((6-x^2)/5x) = 0
Now, simplify the expression inside the logarithm:
(6-x^2)/5x = 1
6/5 - x^2/5x = 1
6/5 - x/5 = 1
Now, solve for x:
6 - x = 5
x = 1
Therefore, the solution is x = 1.