Final answer:
The question asks for the inverse Laplace transform of the function 5/3 ln (s-10/s+10) using operational theorems. The properties of logarithms and linearity of the Laplace transform are key in approaching the solution.
Step-by-step explanation:
The question involves finding the inverse Laplace transform, designated as L−1, of the given function 5/3 ln (s-10/s+10), where ln(x) indicates the natural logarithm of x. To tackle this problem, we can apply an operational theorem, such as the convolution theorem or properties of the Laplace transform, that deals with logarithmic functions.
First, we should recongnize that we can use properties of logarithms to simplify the expression. According to logarithm properties, ln(a/b) = ln(a) - ln(b). Using this, we can rewrite our expression as L−1[5/3 (ln(s-10) - ln(s+10))]. Then, we can look for a standard inverse Laplace transform that matches our manipulations or apply partial fraction decomposition if necessary.
Unfortunately, without additional context or specific operational theorems provided, a detailed step-by-step solution cannot be offered here. However, the general approach would involve looking up or deriving the inverse Laplace transforms of ln(s-10) and ln(s+10), and then applying linearity and scaling properties to address the 5/3 coefficient.