SOLUTION: log base 3 (x) = log base 3 (1/x)+4 i understand that log base 3 (1/x) is subtracted so the problem could look something like this log base 3 (x) -log base 3 (1/x)=4 have one

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log base 3 (x) = log base 3 (1/x)+4 i understand that log base 3 (1/x) is subtracted so the problem could look something like this log base 3 (x) -log base 3 (1/x)=4 have one      Log On


   

Question 187879: log base 3 (x) = log base 3 (1/x)+4
i understand that log base 3 (1/x) is subtracted so the problem could look something like this log base 3 (x) -log base 3 (1/x)=4
have one question doesnt 1 and x become log base 3 (1)- log base 3 (x)
the answer is 9, -9 but i dont know how to set up the problem i am stuck
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




9 certainly could be (and is) the value of x that makes this equation a true statement, but -9 cannot be. The domain of the log function is:



So if you were to say:



What you would really be saying is: "Some undefined thing is equal to some other undefined thing plus 4." A patently absurd thing to say by any measure.

Having said all of that, here's how to do the problem correctly:





Now, use "The log of the quotient is the difference of the logs"



Remove the parentheses and use to write:







Since:



Where whomever gave you the answer of -9 may have gone wrong is they might have said:



And the roots of are 9 and -9, but you still have to go back to the original equation and consider any domain restrictions. Therefore, you must exclude the negative root.

John