Solve the logarithmic equation. (Round your answer to three decimal places.)ln(9x + 7) = 4

Step 1: Understand the equation The equation given is ln(9x + 7) = 4. Here, ln is the natural logarithm, which is the logarithm to the base e, where e is an irrational and transcendental number approximately equal to 2.718281828459.

Step 2: Remove the logarithm To remove the logarithm from the equation, we can use the property of logarithms that says if ln(a) = b, then e^b = a. Applying this to our equation gives us e^4 = 9x + 7.

Step 3: Simplify the equation e^4 is approximately 54.598150033144236. So, the equation simplifies to 54.598150033144236 = 9x + 7.

Step 4: Solve for x Subtract 7 from both sides of the equation to isolate the term with x on one side: 54.598150033144236 - 7 = 9x. This simplifies to 47.598150033144236 = 9x. Then, divide both sides of the equation by 9 to solve for x: 47.598150033144236 / 9 = x.

Step 5: Calculate the value of x Using a calculator, we find that x = 47.598150033144236 / 9 = 5.288683337016026.

Step 6: Round the answer Rounding to three decimal places, we get x = 5.289.