Log0,2 (x+1,5)/ log0,2 100-log0,2 4 <1

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To solve this inequality, we need to use properties of logarithms to simplify the expression.

First, we can rewrite the inequality as:

log0.2 (x+1.5) / (log0.2 100 - log0.2 4) < 1

Next, we can use the property of logarithms that states log_a (b) - log_a (c) = log_a (b/c). Applying this property, we have:

log0.2 ((x+1.5) / 100*4) < 1

log0.2 ((x+1.5) / 400) < 1

Now, we can rewrite the inequality in exponential form:

0.2^1 < (x+1.5) / 400

0.2 < (x+1.5) / 400

Multiply both sides by 400:

80 < x + 1.5

Subtract 1.5 from both sides:

78.5 < x

Therefore, the solution to the inequality is x > 78.5.