Final answer:
The solution set for ln(x - 3) + ln(x - 2) = ln(2x + 24) can be found by using logarithmic properties. The equation (x - 3)(x - 2) = 2x + 24 can be solved to find the values of x that satisfy the equation. The solution set is x = 0.0216 or x = -0.0224.
Step-by-step explanation:
The solution set for ln(x - 3) + ln(x - 2) = ln(2x + 24) can be found by using logarithmic properties. First, we can use the property that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers. So, ln(x - 3) + ln(x - 2) simplifies to ln((x - 3)(x - 2)).
Next, we can use the property that the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of the two numbers. So, ln((x - 3)(x - 2)) = ln(2x + 24) simplifies to (x - 3)(x - 2) = 2x + 24.
We can now solve the equation (x - 3)(x - 2) = 2x + 24 by expanding, simplifying the equation, and solving for x. The solution set for this equation is x = 0.0216 or x = -0.0224.