Solve for \( x \) \[ 4+\ln (x+4)=6 \]

To solve the equation \( 4+\ln (x+4)=6 \), we first isolate the logarithmic term: \[ \ln(x + 4) = 6 - 4 \] \[ \ln(x + 4) = 2 \] Next, we exponentiate both sides to eliminate the natural logarithm: \[ x + 4 = e^2 \] Now, we solve for \( x \) by subtracting 4 from both sides: \[ x = e^2 - 4 \] To find the approximate value, we can use \( e \approx 2.718 \), so: \[ e^2 \approx (2.718)^2 \approx 7.389 \] Thus, \[ x \approx 7.389 - 4 \approx 3.389 \] So, the solution is: \[ x \approx 3.39 \]