Log2(1−х) + log2(3−х)=√3

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To solve this equation, we can use the properties of logarithms and simplify it step by step.

Given:
log2(1-x) + log2(3-x) = √3

Using the properties of logarithms, we can combine the two logarithms on the left side of the equation by using the product rule:

log2((1-x)(3-x)) = √3

Next, simplify the expression inside the logarithm:

log2(3 - x - 3x + x^2) = √3
log2(x^2 - 4x + 3) = √3

Now, we can rewrite the logarithmic equation in exponential form:

2^√3 = x^2 - 4x + 3

Taking the square of both sides:

2^(√3 * 2) = (x^2 - 4x + 3)^2
2^2√3 = (x^2 - 4x + 3)^2
4√3 = x^4 - 8x^3 + 19x^2 - 24x + 9

Now, we have a quartic equation. To solve for 'x', we may need to use numerical methods or approximate the solution.

Unfortunately, there's no simple algebraic solution, and further calculations are necessary to find the exact value of 'x'. Let me know if you need any further assistance.