0,25^(x+3)/(x-2)*30^x*x^-2<=(16^-(x+3)/(x-2)*15^x)/8x^2

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вопрос

To solve this inequality, we need to simplify both sides and then solve for x.

0.25^(x+3)/(x-2)30^xx^-2 <= (16^-(x+3)/(x-2)*15^x)/8x^2

First, let's simplify both sides separately:

Left side:
0.25^(x+3)/(x-2)30^xx^-2
= (25/100)^(x+3)/(x-2)30^x(1/x^2)
= 0.25^(x+3)/(x-2)30^x/x^2
= (25^((x+3)/(x-2)) 30^x) / x^2

Right side:
(16^-(x+3)/(x-2)15^x)/8x^2
= (2^4)^-(x+3)/(x-2)15^x/8x^2
= 2^(-4(x+3)/(x-2)) 15^x/8x^2
= 2^(-(4(x+3)/(x-2))) 15^x/8x^2

Now, the inequality becomes:

(25^((x+3)/(x-2)) 30^x) / x^2 <= 2^(-(4(x+3)/(x-2))) 15^x/8x^2

To solve for x, you can combine the terms, raise both sides to the same power, and then solve for x. The final solution will depend on the value of x obtained from the inequality.