Problem

Solve. \[ \ln (9 x+12)=\ln (8 x+5) \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $x=$ (Simplify your answer. Use a comma to separate answers as needed.) B. There is no solution.

Solution

Step 1 :The natural logarithm function is a one-to-one function, which means that if \(\ln(a) = \ln(b)\), then \(a = b\). Therefore, we can set the arguments of the logarithms equal to each other and solve for \(x\).

Step 2 :So, we have \(9x + 12 = 8x + 5\).

Step 3 :Solving for \(x\), we get \(x = -7\).

Step 4 :The solution to the equation is \(\boxed{-7}\).

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Source: https://solvelyapp.com/problems/39340/

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