Confusing Error in Should-Be-Simple Integration Problem

[Wormaldson]

Homework Statement

Find k such that the area between the function and the x-axis, bounded by x = 1 and x = k, is equal to 100 square units.

Homework Equations

y = 4e^(x/5)

The Attempt at a Solution

1. Wrote the problem as the definite integral from 1 to k of 4e^(x/5)dx = 100.

2. Antidifferentiated to obtain 20e^(x/5).

3. Made substitutions into F(b) - F(a) = 100 to obtain 20e^(k/5) - 20e^(1/5) = 100.

4. Solved for k and got k = 5*ln(5) + 1.

5. At that point I thought I had it all figured out, but when I did 20e^((5*ln(5) + 1)/5) - 20e^(1/5) to check I get 97.7122207 as the result. What am I doing wrong here? Any help would be appreciated.

 

[diazona]

Check your math going from step 3 to step 4. You should be getting a slightly different result for k.

 

[Wormaldson]

Righto, found out what I was doing wrong: I somehow forgot that logs don't distribute over multiplication. How silly of me.

k = 5*ln(5 + e^(1/5))

Edit: Thanks for the help.