How do you simplify e^{\ln x}

widdonod1t

widdonod1t

Answered question

2021-12-12

How do you simplify elnx

Answer & Explanation

Stuart Rountree

Stuart Rountree

Beginner2021-12-13Added 29 answers

Solution: 
So we have: y=elnx 
lny=lnelnxTake ln of both sides 
lny=lnxlne  use the property  logbxn=nlogbx 
lny=lnx(1)lnee=1from the property  log=1 
lny=lnx 
Therefore  y=x

Dabanka4v

Dabanka4v

Beginner2021-12-14Added 36 answers

Let us consider y=eln(x) 
When we apply ln to both sides, we obtain, 
lny=e(1)lnx 
By using the log rule we can write lnex=xln(e) 
ln(y)=ln(x)lne) [ solving RHS of equation 1 and LHS remains same] 
ln(y)=ln(x)[ln(e)=1] 
y will be equal to x as logs with same base are equal. 
As we know from our assumption that y=eln(x) 
Therefore, e to the power of ln can be written as eln(x)=xS

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