ln 1/sqrt e = -1/2 write in exponential form pls show steps ln 1/sqrt e = -1/2 write in exponential form pls show steps @Mathematics

Question

anonymous · Answer

$$\ln 1/\sqrt{e} =-1/2$$

agreene · Answer

$$\ln \frac1{\sqrt e}=-\frac12$$
$$\ln e^{-\frac12}=-\frac12$$
$$\cancel \ln \cancel e^{-\frac12}=-\frac12$$
$$-\frac12=-\frac12$$
$$QED$$

anonymous · Answer

what is QED?

agreene · Answer

"quod erat demonstrandum"

agreene · Answer

Or, "Thus I have shown"
Its a way of ending a proof.

anonymous · Answer

ahh.  i thought it was a cool answer.

agreene · Answer

http://en.wikipedia.org/wiki/Q.E.D. :)

anonymous · Answer

so 1/sqrt e is e^-1/2?  or conversly, 1/sqrt a is a^-1/n?

agreene · Answer

$$\frac1a  ≡ a^{-1}$$
and
$$\sqrt{a} ≡ a^{1/2}$$
therefore:
$$\large\frac1{\sqrt a} = a^{-\frac12}$$

anonymous · Answer

nice.  thanks for your help.  I struggled the first month in algebra.. really paying for it now with exponents and radicals.. especially with rational exponents

agreene · Answer

Whereas:
$$\huge\sqrt[n]a ≡a^{\frac1n}$$
and thus:
$$\huge\frac{1}{\sqrt[n]a}=a^{-\frac1n}$$

and no problem :)

anonymous · Answer

Ill have to add these to my big retriceformula sheet that I am trying to memorize!

agreene · Answer

hehe, once you get the hang of how some of these things work (this one especially) it will make your life a lot easier, because you'll see much easier ways of doing things than if you thought you were forced to use a fraction (you can just take it to a negative power ;) )