Final answer:
To solve the equation e^2 = 32, we take the natural logarithm of both sides and isolate the variable. This leads to e = sqrt(32), which is approximately 5.6569. Rounding to the nearest whole number, the solution is 6.
Step-by-step explanation:
The student is asking to solve the exponential equation e^2 = 32 and to estimate the solution to the nearest whole number. To solve this equation, we can take the natural logarithm of both sides to isolate the variable. This gives us:
ln(e^2) = ln(32)
Since the natural logarithm and the exponential function are inverse functions, ln(e^2) simplifies to 2, and the equation becomes:
2 = ln(32)
We can then divide both sides by 2 to find the value of e:
e = sqrt(32)
Using a calculator, we find that sqrt(32) is approximately 5.6569. Rounding this to the nearest whole number gives us 6 as the solution.