Log0,5(x^2-5x)>log0,5(2x-3)

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In order to solve this inequality, we must rewrite it in exponential form. We know that:

log0,5(a) = b is equivalent to a = (0,5)^b

Therefore, the inequality becomes:

x^2 - 5x > (0,5)^(2x-3)

Now we can use the property of logarithms which states that if loga(b) > loga(c), then b > c. Applying this property to our inequality, we get:

x^2 - 5x > 2x - 3

Rearranging the terms, we get:

x^2 - 7x + 3 > 0

Now we need to solve this quadratic inequality. The solutions are x < 0,33 or x > 6. Therefore, the solution to the original inequality is x < 0,33 or x > 6.