To solve the inequality (3^x - 9) * log3(x + 4) > 0, we need to consider the cases when the expression is positive.
First, let's analyze the factors in the expression:
(3^x - 9) can be positive when 3^x > 9, which means x > log3(9) = 2, as 3^2 = 9. So, this factor is positive for x > 2.
log3(x + 4) is positive when x + 4 > 1, which means x > -3. Therefore, this factor is positive for x > -3.
Now, we need to consider the combined effect of both factors being positive. This happens when x > 2 and x > -3, which simplifies to x > 2. So, the inequality (3^x - 9) * log3(x + 4) > 0 holds true for x > 2.
To solve the inequality (3^x - 9) * log3(x + 4) > 0, we need to consider the cases when the expression is positive.
First, let's analyze the factors in the expression:
(3^x - 9) can be positive when 3^x > 9, which means x > log3(9) = 2, as 3^2 = 9. So, this factor is positive for x > 2.
log3(x + 4) is positive when x + 4 > 1, which means x > -3. Therefore, this factor is positive for x > -3.
Now, we need to consider the combined effect of both factors being positive. This happens when x > 2 and x > -3, which simplifies to x > 2. So, the inequality (3^x - 9) * log3(x + 4) > 0 holds true for x > 2.