How do I solve #3^(2x) - 5(3^x)=-6#? Precalculus Properties of Logarithmic Functions Common Logs 1 Answer sjc Oct 16, 2017 #x=1# or #:.x=(log2)/(log3)~~0.6309297536# Explanation: #3^(2x)-5(3^x)=-6# let #u=3^x# then we have #u^2-5u=-6# #=>u^2-5u+6=0# a quadratic in #u# #(u-3)(u-2)=0# #:.u=2, " or "u=3# #u=3 "gives "3^x=3=>x=1# #u=2 " gives "3^x=2# #3^x=2# take logs #log(3^x)=log2# #xlog3=log2# #:.x=(log2)/(log3)~~0.6309297536# 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 5633 views around the world You can reuse this answer Creative Commons License