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.
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.