evgen_pro

Let's simplify the equation step by step: First, we can combine the first two terms using the quotient rule of logarithms: log²2x - 4log2x + 3 = log₂((2x)² / 2⁴) + 3 = log₂(x² / 16) + 3 Now we can use the fact that log₂(a) + log₂(b) = log₂(ab) to combine the terms inside the logarithm: log₂(x² / 16) + 3 = log₂(x²) - log₂(16) + 3 = 2log₂(x) - 4 + 3 = 2log₂(x) - 1 So our equation becomes: 2log₂(x) - 1 = 0 We can solve for log₂(x) by adding 1 to both sides: 2log₂(x) = 1 log₂(x) = 1/2 Finally, we can solve for x by taking the inverse logarithm of both sides: x = 2^(log₂(x)) = 2^(1/2) = √2 Therefore, the solution to the equation is x = √2.