Question

Write as the sum and or diff of logs
ln sq root ex

Answer 1

\[\large \sqrt{e^x}?\]

Answer 2

\[\ln(\sqrt{ex})=\frac{1}{2}\ln(ex)=\frac{1}{2}\left(\ln(e)+\ln(x)\right)\]
last step is to compute \(\ln(e)\)

Answer 3

Still don't really understand, what would the sum or difference of logs be? To be more clear the question is : ln sq root ex

Answer 4

you are using four facts:
\(\sqrt{ex}=(ex)^{\frac{1}{2}}\)
\(\ln(x^n)=n\ln(x)\)
\(\ln(ab)=\ln(a)+\ln(b)\)
and finally \(\ln(e)=1\)

Answer 5

So it would end up being 1/2 +ln(x)?

Answer 6

don't forget the distributive law
it would be
\[\frac{1}{2}+\frac{1}{2}\ln(x)\]

Answer 7

Oh okay and that would be the answer?

Answer 8

yes