SOLUTION: PLEASE SHOW ME HOW TO SOLVE THIS PROBLEM, I HAVE AN EXAM TOMORROW AND I NEED TO KNOW HOW TO DO THESE BASIC PROBLEMS. ln√e, please solve without a calculator! AND LOG√2(

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: PLEASE SHOW ME HOW TO SOLVE THIS PROBLEM, I HAVE AN EXAM TOMORROW AND I NEED TO KNOW HOW TO DO THESE BASIC PROBLEMS. ln√e, please solve without a calculator! AND LOG√2(      Log On


   

Question 444093: PLEASE SHOW ME HOW TO SOLVE THIS PROBLEM, I HAVE AN EXAM TOMORROW AND I NEED TO KNOW HOW TO DO THESE BASIC PROBLEMS. ln√e, please solve without a calculator! AND LOG√2(4)a tutor tried to help me with the last one but im still very lost.
thank you!
Found 2 solutions by chriswen, ankor@dixie-net.com:
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
ln √ e
=lne%5E%281%2F2%29
=%281%2F2%29lne
=1%2F2
since ln e = 1.
So ln root e =1/2
Log [√ 2 (4)] right?
=log √ 2 +log 4
=log 2^(1/2)+log 4
=log 2^(1/2)+log 2^2
=log [2^(1/2)*2^2]
=log 2^(2.5)
You can use a calculator for that right? Since it calculates to around .49 . Hope that helps.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28sqrt%28e%29%29
you know that you can write the square root as an exponent
ln%28e%5E%281%2F2%29%29
Write the log equiv of exponents:
%281%2F2%29%2Aln%28e%29
you know the ln of e = 1
%281%2F2%29%2A1 = 1%2F2
:
logsqrt%282%29%284%29, Assume this means the log basesqrt%282%29 of 4?
:
remember the log of the number is equal to exponent of the base
using common logs as an example, log,base10(1000) = 10^3, log is 3
:
In this problem, what exponent of sqrt%282%29 is 4
2 * 2 = 4, therefore
sqrt%282%29*sqrt%282%29*sqrt%282%29*sqrt%282%29 = 4
or we can say sqrt%28%282%29%29%5E4 = 4
therefore
logsqrt%282%29%284%29 = 4?