Log0,2(x-2)+log0,2x>log0,2(2x-3)

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To solve this inequality, we can combine the logarithms using the properties of logarithms.

First, we can combine the logarithms on the left side of the inequality using the product rule of logarithms:

log0.2[(x-2)x] > log0.2(2x-3)

Now, we simplify the logarithm on the left side by multiplying the terms inside the logarithm:

log0.2(x^2 - 2x) > log0.2(2x-3)

Since the bases are the same, we can drop the logarithms and set the terms inside each logarithm equal to each other:

x^2 - 2x = 2x - 3

Now, we solve the equation for x:

x^2 - 4x + 3 =
(x-3)(x-1) = 0

Solution: x = 3 or x = 1

Therefore, the solutions to the inequality log0.2(x-2) + log0.2x > log0.2(2x-3) are x = 3 and x = 1.