How do you calculate # log_5(4) #? Precalculus Properties of Logarithmic Functions Common Logs 1 Answer Shwetank Mauria Apr 8, 2016 #log_5(4)=0.8614# Explanation: Let #log_ba=x#, then #b^x=a#. If #a=10^n# and #b=10^m#, then #n=loga# and #m=logb# and #b^x=a# becomes #(10^m)^x=10^n# or #10^(mx)=10^n# i.e. #mx=n# Hence #x=n/m=loga/logb# Thus #log_5(4)=log4/log5=0.6021/0.6990=0.8614# 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 1575 views around the world You can reuse this answer Creative Commons License