# 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?)

**sqrt(x)/x
(isn't that already simplified?)**

I agree with you.

you could do this: x^(1/2)/x

= x(-1/2)

= 1/√x but that is certainly not simpler.

**e^(1+lnx)**

(I have no clue.)

(I have no clue.)

e^(1+lnx)

=(e)(e^lnx)

=e(x) = ex

**n(1/2)**

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

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

ln(1/2)

= ln 1 - ln 2

= 0 - ln 2

= -ln 2

**e^(3lnx)**

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

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

yes, based on the fact that a^(log

_{a}k = k

## For e^(3lnx), you can use the property that e^(lnx) = x.

So, we have e^(3lnx) = (e^(lnx))^3 = (x)^3 = x^3.