What is x if #log_3 (x-1) + log_3 (x-9) = 2#? Algebra Exponents and Exponential Functions Applications of Exponential Functions 1 Answer maganbhai P. Apr 4, 2018 #x=10# Explanation: We know that , #color(blue)((1)log_aM+log_aN=log_a(MN)# #color(blue)((2)log_aX=n<=>X=a^n# Here, #log_3(x-1)+log_3(x-9)=2...toApply (1)# #=>log_3((x-1)(x-9))=2...toApply (2)# #=>(x-1)(x-9)=3^2# #=>x^2-x-9x+9=9# #=>x^2-10x=0# #=>x(x-10)=0# #=>x=0 or x-10=0# #=>x=0 or x=10# But, #x=0=>x-1=0-1=-1 < 0# # and x-9=0-9=-9 < 0# So,#x!=0# i.e. #x=10# Answer link Related questions How do you know if a word problem is talking about exponential functions? What are some Applications of Exponential Functions? What percent of a substance is left after six hours if a radioactive substance decays at a rate... How many bird species will there be left in the year 2020 if in 1990, a rural area had 1200 bird... What is the total amount in the account after 12 years if Peter invests $360 in an account that... How do you determine the exponential function for a half life problem? How many bacteria would be present 15 hours after the experiment began if a set of bacteria... How many bacteria will be present after 5 hours if a culture of bacteria obeys the law of... If the length of a side of a cube is 4x, what is the volume of the cube? Why can't you have zero to the power of zero? See all questions in Applications of Exponential Functions Impact of this question 1857 views around the world You can reuse this answer Creative Commons License