How do you use the properties of logarithms to expand #lnroot3(x^2/y^3)#? Precalculus Properties of Logarithmic Functions Common Logs 1 Answer Somebody N. Jul 2, 2018 #color(blue)(2/3lnx-lny)# Explanation: #root(3)(x^2/y^3)=(x^2/y^3)^(1/3)# By the laws of logarithms: #lna^b=blna# #ln(a/b)=lna-lnb# Hence: #ln(x^2/y^3)^(1/3)=1/3ln(x^2/y^3)=1/3ln(x^2)-1/3ln(y^3)# # \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \=2/3lnx-3/3lny# # \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \=2/3lnx-lny# Answer link Related questions What is the common logarithm of 10? How do I find the common logarithm of a number? What is a common logarithm or common log? What are common mistakes students make with common log? How do I find the common logarithm of 589,000? How do I find the number whose common logarithm is 2.6025? What is the common logarithm of 54.29? What is the value of the common logarithm log 10,000? What is #log_10 10#? How do I work in #log_10# in Excel? See all questions in Common Logs Impact of this question 1702 views around the world You can reuse this answer Creative Commons License