Is this possible without a calculator?

[Procrastinate]

I was doing this problem about optimization and I derived it to:

R' = (1-lnx)/x²

(This was the right derivative by the way as the maximum on the R function was the same answer as when R' = 0)Anyways as R' = 0 when stationary points occur:

0 = (1-lnx)/x²

I was wondering whether it was possible to do that without the help of a graph/graphics calculator because of the zero there. I managed to get the correct answer which was x=2.71 but I couldn't do it manually because of the zero even when I used the null factor law (1-lnx) = 0 or 1/x² = 0.

 

[Phrak]

2.718281828... is the base of the natural log.

Plug ln(x) = 2.718281828 into your calculator. The answer should be close to 1.

 

[rl.bhat]

I was doing this problem about optimization and I derived it to:

R' = (1-lnx)/x²

(This was the right derivative by the way as the maximum on the R function was the same answer as when R' = 0)


Anyways as R' = 0 when stationary points occur:

0 = (1-lnx)/x²

(1-lnx) = 0 or 1/x² = 0.

1-lnx=0 or lnx = 1

$$lnx = \log_e{x} = 1$$

It is true when x = e = 2.71.

 

[Procrastinate]

Thank you.