Solve for $y$ in the equation below.
Round your answer to the nearest hundredth. Do not round any intermediate computations.
\[
e^{y-3}=4
\]

Answer

Expert–verified

Hide Steps

Answer

So, the solution to the equation $e^{y-3}=4$ is $y = \boxed{4.39}$.

Steps

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 $y = \boxed{4.39}$.