How do you simplify e^{-\ln x}

Monique Slaughter

Monique Slaughter

Answered question

2021-12-13

How do you simplify elnx

Answer & Explanation

zesponderyd

zesponderyd

Beginner2021-12-14Added 41 answers

Use it for solution:
Consider the generic case of log10(a)=b
Another way of writing this is 10b=a
Suppose a=10log10(10)=b
10b=10b=1
So loga(a)=1 - important example
use this principle

Serita Dewitt

Serita Dewitt

Beginner2021-12-15Added 41 answers

Write elnx as 1elnx
Let y=elnx1y=1elnx...Equation (1)
Consider just the denominators and take logs of both sides
y=elnxln(y)=ln(eln(x))
But for generic case ln(st)tln(s)
ln(y)=ln(x)ln(e)
But loge(e)ln(e)=1
ln(y)=ln(x)×1
Thus y=x
So Equation(1) becomes
1y=1eln(x)=1x
Thus elnx=1x

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