Proof of Logarithims (1 Viewer)

[Justplainbored]

how do u prove that

....loge x
e....= x

and just in case u dont get what it says

its e to the power of logx base e = x
e^logx =x

 

[oly1991]

e^lnx=x
ln(e^lnx)=lnx (logging both sides)
lnxlne=lnx (log laws)
lnx=lnx (lne=1)
x=lnx/ln
=x
therefore LHS=RHS

im not sure if that's 100% right but im pretty sure thats how u do it.

 

[gurmies]

 

[oly1991]

i cant see how thats proving anything

 

[gurmies]

i cant see how thats proving anything

Look closer...

 

[Drongoski]

how do u prove that

....loge x
e....= x

and just in case u dont get what it says

its e to the power of logx base e = x
e^logx =x

The functions log_e and 'e to the power of' are inverses of each other. When you take log_e of x and then exponentiate it (e to the power of log_e x) the 2nd function "edit undo" the first one thereby undoing the transformation by the log_e giving you back the original x.

In the same way: log_e e^x = x

 

[oly1991]

Look closer...

oh yes i see

 

[Trebla]

If you happen to do Ext1, then this is just using f^-1[f(x)] = x, where f^-1(x) is the inverse function of f(x).