SOLUTION: Given x = log_b 8 , y = log_b 3, I have to express the answer in terms of x and y. log_3b (8/9) is the given equation. I got up to log_3b 8 - 2 log_3b 3, currently wondering

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given x = log_b 8 , y = log_b 3, I have to express the answer in terms of x and y. log_3b (8/9) is the given equation. I got up to log_3b 8 - 2 log_3b 3, currently wondering      Log On


   

Question 993329: Given x = log_b 8 , y = log_b 3, I have to express the answer in terms of x and y.
log_3b (8/9) is the given equation.
I got up to log_3b 8 - 2 log_3b 3, currently wondering how do I change the base 3b to b, but the base is a variable so I'm not sure how to do so.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
system%28log%28b%2C8%29=x%2Clog%28b%2C3%29=y%29

You want to simplify the expression, highlight_green%28log%283b%2C%288%2F9%29%29%29
log%283b%2C8%29-log%283b%2C9%29
Change Of Base Formula gives
log%28b%2C8%29%2Flog%28b%2C3b%29-log%28b%2C9%29%2Flog%28b%2C3b%29
log%28b%2C8%29%2Flog%28b%2C3b%29-log%28b%2C%283%5E2%29%29%2Flog%28b%2C3b%29
log%28b%2C8%29%2Flog%28b%2C3b%29-2%2Alog%28b%2C3%29%2Flog%28b%2C3b%29
Substitute your given relationships,
x%2Flog%28b%2C3b%29-2%2Ay%2Flog%28b%2C3b%29
%28x-2y%29%2Flog%28b%2C3b%29

Next deal with the denominator,
%28x-2y%29%2F%28log%28b%2C3%29%2Blog%28b%2Cb%29%29
highlight%28%28x-2y%29%2F%28y%2B1%29%29