Problem
Solve for $y$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ e^{y-3}=4 \]
Solution
Step 1 ：Take the natural logarithm (ln) of both sides of the equation \(e^{y-3}=4\). This gives us \(y-3 = ln(4)\).
Step 2 ：Add 3 to both sides of the equation to solve for y. This gives us \(y = ln(4) + 3\).
Step 3 ：Using a calculator, we find that \(ln(4) + 3\) is approximately 4.39.
Step 4 ：So, the solution to the equation \(e^{y-3}=4\) is \(y = \boxed{4.39}\).
