To solve this inequality, we need to first understand that log0,2 means logarithm base 0.2.
So, the given inequality is:
log0,2(2x-6) > log0,2(x² + 3)
Now, we can use the property of logarithms that if loga(b) > loga(c), then b > c.
Therefore, in this case:
2x - 6 > x² + 3
Rearranging the terms, we get:
0 > x² - 2x + 9
Now, we can try to solve for x by setting the expression on the right side to zero:
x² - 2x + 9 = 0
We can factor this equation or use the quadratic formula to solve for x.
After finding the values of x, we can determine the intervals where the inequality holds true based on the solutions of the quadratic equation.
To solve this inequality, we need to first understand that log0,2 means logarithm base 0.2.
So, the given inequality is:
log0,2(2x-6) > log0,2(x² + 3)
Now, we can use the property of logarithms that if loga(b) > loga(c), then b > c.
Therefore, in this case:
2x - 6 > x² + 3
Rearranging the terms, we get:
0 > x² - 2x + 9
Now, we can try to solve for x by setting the expression on the right side to zero:
x² - 2x + 9 = 0
We can factor this equation or use the quadratic formula to solve for x.
After finding the values of x, we can determine the intervals where the inequality holds true based on the solutions of the quadratic equation.