SOLUTION: log5 how to solution with out using calculater

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Question 1074994: log5 how to solution with out using calculater
Found 3 solutions by addingup, Edwin McCravy, ikleyn:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
You solve logarithms with exponentials, here is the relationship, assuming you mean the natural logarith of 5.
:
The base of a natural logarithm is e (the number e, 2.718...)
therefore:
log_b(x) = y
b^ŷ = x
log_e 5 = y
e^ŷ = 5
or if you want to use the numerical equivalent of e to three decimals:
2.718^ŷ = 5
Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!
There is no way other than approximation by series or
iterative methods, because it is an irrational number.

0.6989700043360188047862611052755069732318101185378914586895725388728918107255754905130727478818138279593155228085690046209052321188664764940003076662953044249354970357458065973381802656883970564988160971018214173828455604681380...

The "solution" above uses e, but there is no way to find
e other than by approximation by series or iterative
methods, because it is an irrational number. It only uses
e to 3 decimal places.  
Edwin
Answer by ikleyn(52906)   (Show Source): You can put this solution on YOUR website!
.
Without using a calculator, you may look to trigonometric tables
(as your grandfather and grandmother did in pre-computer era)
or to the Internet.



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