How do you condense #1/3ln x + ln y#? Precalculus Properties of Logarithmic Functions Natural Logs 1 Answer Shwetank Mauria Apr 14, 2016 #1/3lnx+lny=ln(yroot(3)x)# Explanation: We can condense using identities #log_ap_1+log_ap_2+log_ap_3+..+log_ap_n=log_a(p_1*p_2*p_3*...*p_n)# and #nlog_ap=log_ap^n# and #1/mlog_ap=log_ap^(1/m)=log_aroot(m)p# Using these #1/3lnx+lny=lnroot(3)x+lny=ln(yroot(3)x)# 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 3374 views around the world You can reuse this answer Creative Commons License