To solve the expression 13 ln x + 23 – 12 ln x + ln(x^2) + 3x – 22, we start by simplifying the terms that involve natural logarithms and constant values.
First, let’s combine the logarithmic terms:
- 13 ln x – 12 ln x + ln(x^2) = (13 – 12) ln x + ln(x^2) = 1 ln x + 2 ln x = 3 ln x
Now, we can rewrite ln(x^2) as 2 ln x. So we can simplify the expression to:
- 3 ln x + 23 – 22 + 3x = 3 ln x + 1 + 3x
Thus, our final expression becomes:
- 3 ln x + 3x + 1
This is the simplified form of the original expression. To find specific solutions, we would typically set this expression equal to zero or a specific value, depending on the context of the problem.