Solve the logarithmic equation. \[ \ln (9 x+8)-\ln x=\ln 10 \] What is the equivalent algebraic equation that must be solved? A. $(9 x+8) x=e^{10}$ B. $\frac{9 x+8}{x}=10$ C. $\frac{9 x+8}{x}=e^{10}$ D. $(9 x+8) x=10$

Step 1 ：\(\ln (9 x+8)-\ln x=\ln 10\)

Step 2 ：Using the properties of logarithms, rewrite the equation as \(\ln \left(\frac{9 x+8}{x}\right)=\ln 10\)

Step 3 ：Since the natural logarithm is a one-to-one function, equate the arguments of the logarithms to get the equivalent algebraic equation: \(\frac{9 x+8}{x}=10\)

Step 4 ：So, the final answer is \(\boxed{\frac{9 x+8}{x}=10}\)