Solve the following logarithmic equation. Use a calculator if appropriate.
\[
\log (3 x+1)+\log 2=\log (5 x+6)
\]
Answer
Solve the linear equation for x to get the final answer. The solution to the logarithmic equation is \(\boxed{4}\).
Step 1 ：Combine the left side of the equation using the property of logarithms that states that the sum of two logarithms (with the same base) is equal to the logarithm of the product of their arguments. This gives us \(\log (6x + 2) = \log (5x + 6)\).
Step 2 ：Use the property of logarithms that states that if two logarithms (with the same base) are equal, then their arguments are also equal. This gives us the simple linear equation \(6x + 2 = 5x + 6\).
Step 3 ：Solve the linear equation for x to get the final answer. The solution to the logarithmic equation is \(\boxed{4}\).
