Question

I am suppose to simplify the following problems:

sqrt(x)/x
(isn't that already simplified?)
e^(1+lnx)
(I have no clue.)
ln(1/2)
(I know this problem translates--> e^x=1/2--> but how would you solve it w/o a calculator?)
e^(3lnx)
([e^(lnx^3)]--> is it equal to 3?)

<b>sqrt(x)/x
(isn't that already simplified?)</b>

I agree with you.
you could do this: x^(1/2)/x
= x(-1/2)
= 1/√x but that is certainly not simpler.

<b>e^(1+lnx)
(I have no clue.) </b>

e^(1+lnx)
=(e)(e^lnx)
=e(x) = ex

<b>n(1/2)
(I know this problem translates--> e^x=1/2--> but how would you solve it w/o a calculator?) </b>

ln(1/2)
= ln 1 - ln 2
= 0 - ln 2
= -ln 2

<b> e^(3lnx)
([e^(lnx^3)]--> is it equal to 3?)</b>

yes, based on the fact that a^(log_a k = k