SOLUTION: How do I find ln sixth root of e without a calculator? My options for answers is 1/e , 6, 1/6, or e. Thank you so much for explaining how to execute this. I'm not sure if we can ca

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do I find ln sixth root of e without a calculator? My options for answers is 1/e , 6, 1/6, or e. Thank you so much for explaining how to execute this. I'm not sure if we can ca      Log On


   

Question 917285: How do I find ln sixth root of e without a calculator? My options for answers is 1/e , 6, 1/6, or e. Thank you so much for explaining how to execute this. I'm not sure if we can cancel the ln and e if the e is under the square root.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
e%5E%281%2F6%29

No Calculator? Table of Natural logarithms!

e%5E%281%2F6%29=N
ln%28e%5E%281%2F6%29%29=ln%28N%29
%281%2F6%29%2A1=ln%28N%29
Use the table to find or determine natural log of 1%2F6.


(1.181, but I used a calculator.)

Here is an online table:
http://myhandbook.info/table_naperlog.html

The mantissa nearest to 1%2F6 is 0.165514.
This is for log of 1.800.
What you want is between 1.8 and 1.9;
Use linear interpolation to get a more accurate value.

N_______________Natural Logarithm
1.800___________0.165514
v_______________0.16666666666...
1.900___________0.173953


The choices which you say from which you must choose are all equally bad.