How do you condense #2/3ln y + ln t – ln y -1/2 ln t#? Precalculus Properties of Logarithmic Functions Natural Logs 1 Answer Shwetank Mauria Sep 2, 2016 #2/3lny+lnt-lny-1/2lnt=ln(sqrtt/(root(3)y))# Explanation: #2/3lny+lnt-lny-1/2lnt# = #lny(2/3-1)+lnt(1-1/2)# = #-1/3lny+1/2lnt# Now as #1/mlna=lna^(1/m)=lnroot(m)a# and #-lnb=ln(1/b)# #-1/3lny+1/2lnt# = #ln(1/root(3)y)+lnsqrtt# = #ln(sqrtt/(root(3)y))# Answer link Related questions What is the natural log of e? What is the natural log of 2? How do I do natural logs on a TI-83? How do I find the natural log of a fraction? What is the natural log of 1? What is the natural log of infinity? Can I find the natural log of a negative number? How do I find a natural log without a calculator? How do I find the natural log of a given number by using a calculator? How do I do natural logs on a TI-84? See all questions in Natural Logs Impact of this question 1338 views around the world You can reuse this answer Creative Commons License