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.)
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?)
ln(1/2)
= ln 1 - ln 2
= 0 - ln 2
= -ln 2
e^(3lnx)
([e^(lnx^3)]--> is it equal to 3?)
yes, based on the fact that a^(loga 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.