SOLUTION: Hello, We are learning logarithms in my math class and the exam is next week and one of the problems we are supposed to know is how to write {{{ log( 9, sqrt(x))-log( 3, x^3)}}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello, We are learning logarithms in my math class and the exam is next week and one of the problems we are supposed to know is how to write {{{ log( 9, sqrt(x))-log( 3, x^3)}}}      Log On


   



Question 857039: Hello,
We are learning logarithms in my math class and the exam is next week and one of the problems we are supposed to know is how to write +log%28+9%2C+sqrt%28x%29%29-log%28+3%2C+x%5E3%29 as a single log expression in base 3 but I can't figure out how to do it. I've been trying to use the change of base rule where log%28y%2Cx%29+=+log%28x%29%2Flog%28y%29 in base 10 and using that i was able to put it into the form of +log%28sqrt%28x%29%29%2Flog%289%29+-+log%28x%5E3%29%2Flog%283%29+ but I don't know how to change the base so they both have base 3.
Could you help me figure this out please?

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
2log(3, sqrt(x))=log( 9, sqrt(x))