Thread: finding simpler expressions for the quantities

i'm just not seeing it for these:
ln(e^(e^(x))
and
ln(e^(2lnx)

i don't know where to begin!
and is this one correct
ln(e^secx)= ln(e)^secx= secxlne=secx

Originally Posted by genlovesmusic09

i'm just not seeing it for these:
ln(e^(e^(x)) = e^x
and
ln(e^(2lnx) = ln x^2

i don't know where to begin!
and is this one correct
ln(e^secx)= secx

ln and e are inverses so they reduce y=x. Does this make sense? Ienteredthe right answers in for you

Hello genlovesmusic09

Originally Posted by genlovesmusic09

i'm just not seeing it for these:
ln(e^(e^(x))
and
ln(e^(2lnx)

i don't know where to begin!
and is this one correct
ln(e^secx)= ln(e)^secx= secxlne=secx

Two of the basic properties of logarithms (to any base, $\displaystyle a$) are:

• $\displaystyle \log_a(p^q)=q\log_a(p)$

• $\displaystyle \log_a(a)=1$, and in particular, $\displaystyle \ln(e)=1$

So, if we apply these to your two questions:

$\displaystyle \ln(e^{(e^x)})=e^x\ln(e)=e^x$

and $\displaystyle \ln(e^{2\ln (x)})=2\ln (x)\ln(e)=2\ln(x)$, which you can write as $\displaystyle \ln(x^2)$ if you like (again using the first of these laws).

Grandad