Solve the equation $\ln (7 x+5)=1$
The exact solution (using exponents) is $x=\frac{e-5}{7}$

The solution, rounded to 4 decimal places is $x=$

Step 1 ：Solve the equation \( \ln (7 x+5)=1 \)

Step 2 ：Use the property of logarithms that says the logarithm base e of a number is the exponent to which e must be raised to equal that number. Therefore, we can rewrite the equation as \( 7x + 5 = e^1 \)

Step 3 ：Solve this equation for x to get the exact solution \( x=\frac{e-5}{7} \)

Step 4 ：Calculate the value of e and perform the necessary operations to find the solution rounded to 4 decimal places, which is \( x = -0.325959738791565 \)

Step 5 ：Round the solution to 4 decimal places to get \( x = -0.326 \)

Step 6 ：Final Answer: The solution to the equation \( \ln (7 x+5)=1 \), rounded to 4 decimal places, is \( x=\boxed{-0.326} \)