To find the product of the functions f(x) and g(x), we start by defining these functions more clearly:
- f(x) = log2(3x + 9)
- g(x) = log2(x + 3)
The product of these two functions, denoted as f(x) * g(x), can be expressed as follows:
f(x) * g(x) = log2(3x + 9) * log2(x + 3)
Now, let’s analyze this step by step:
- First, we compute each function for a specific value of x. For example, let’s take x = 1:
- f(1) = log2(3*1 + 9) = log2(12)
- g(1) = log2(1 + 3) = log2(4) = 2
- Now, we can calculate the product:
- f(1) * g(1) = log2(12) * 2
- This product depends on the logarithmic values:
- We know that log2(12) isn’t a nice round number, but it can be calculated. We can approximate it:
- log2(12) ≈ 3.585 (using a calculator or logarithm table)
- Now we multiply:
- f(1) * g(1) ≈ 3.585 * 2 ≈ 7.17
Thus, we find that for x = 1, f(x) * g(x) is approximately 7.17.
In conclusion, the product of the two functions, f(x) and g(x), expressed as log2(3x + 9) * log2(x + 3), captures various values depending on x. To get a comprehensive understanding, evaluate the product for various x values and analyze how the logarithmic properties influence the overall product.