How do you solve #log_4x=log_8(4x)#? Precalculus Properties of Logarithmic Functions Common Logs 1 Answer Cesareo R. Aug 23, 2016 #x = 2^4# Explanation: Using #log_a b= log_e a/(log_e b)# #log_4x = (log_e x)/(log_e 4) = log_8(4x) = (log_e (4x))/(log_e 8)# but #log_e 4 = 2 log_e 2# and #log_e 8 = 3 log_e 2# so #log_e x/(2log_e 2) = (log_e x + 2log_e 2)/(3 log_e 2)# #3log_e x = 2log_e x+4 log_e 2# and finally #log_e x = log_e 2^4# so #x = 2^4# 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 3216 views around the world You can reuse this answer Creative Commons License