Solve the cquation. Witte the solution set with the exact values given in terms of common or natural logarthms, Alse glve approximato solutions to at least 4 decimal places. \[ 3 e^{3 m-2}-4=11 \]

Step 1 ：Given the equation \(3 e^{3 m-2}-4=11\)

Step 2 ：Add 4 to both sides of the equation to get rid of the -4 on the left side, resulting in \(3 e^{3 m-2}=15\)

Step 3 ：Divide both sides by 3 to isolate the exponential term, resulting in \(e^{3 m-2}=5\)

Step 4 ：Take the natural logarithm of both sides to get rid of the exponential term, resulting in \(3 m-2=\ln(5)\)

Step 5 ：Solve for 'm' by adding 2 to both sides and then dividing by 3, resulting in \(m=\frac{\ln(5)+2}{3}\)

Step 6 ：The exact solution to the equation is \(m=\frac{\ln(5)+2}{3}\)

Step 7 ：Approximate the solution to at least 4 decimal places, resulting in \(m \approx 1.2031\)

Step 8 ：\(\boxed{m \approx 1.2031}\) is the final answer