Solve for #x#, given #x^((log_5 x)-2) = (x^2/(125))# ? Precalculus Properties of Logarithmic Functions Common Logs 1 Answer Cesareo R. Oct 23, 2017 #x = {5,125}# Explanation: Applying #log_5# to both sides #(log_5 x-2)log_5 x=2log_5x - 3# and now calling #y = log_5 x# #(y-2)y=2 y-3# or #y^2-4y+3=0# now solving for #y# #y = {1,3}# or #log_5 x = 1 rArr x = 5# and #log_5 x = 3 rArr x = 125# 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 1633 views around the world You can reuse this answer Creative Commons License