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.
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.