How do you condense lny+lntlny+lnt?
1 Answer
Aug 22, 2017
Provided
ln y + ln t = ln (yt)lny+lnt=ln(yt)
Explanation:
Note that if
ln a + ln b = ln (ab)lna+lnb=ln(ab)
This follows from the corresponding property of exponents:
e^(p+q) = e^p * e^qep+q=ep⋅eq
since
So given
p = ln a" "p=lna and" "q = ln b q=lnb .
Then:
e^p = a" "ep=a and" "e^q = b eq=b
So:
ln a + ln b = p + q = ln(e^(p+q)) = ln(e^p * e^q) = ln(ab)lna+lnb=p+q=ln(ep+q)=ln(ep⋅eq)=ln(ab)
So provided
ln y + ln t = ln (yt)lny+lnt=ln(yt)