SOLUTION: prove that e^logx=x
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Question 790521: prove that e^logx=x
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
From the problem context, I am going to presume that "log" with an unspecified base is base 
rather than the more commonly accepted base 10. You will avoid a great deal of ambiguity in the future if you use )
as the natural logarithm function of 
meaning )
and reserve )
to mean )
.
We wish to prove:
}\ =\ x)
Assume
And use algebra to obtain an identity.
Take the natural log of both sides:
}\right)\ =\ \ln(x))
Use the properties of logarithms:
\ =\ n\log_b(x))
and
\ =\ 1)
to write
\left(\ln(e)\right)\ =\ \ln(x))
\ =\ \ln(x))
Which is true for all in the domain of
Therefore }\ =\ x)
is true for all in the domain of .
Q.E.D.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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