SOLUTION: If {{{log(9,5)=x}}} and {{{log(27,2)=y}}}, express {{{log(3,100)}}} in terms of x and y

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If {{{log(9,5)=x}}} and {{{log(27,2)=y}}}, express {{{log(3,100)}}} in terms of x and y      Log On


   

Question 1118207: If log%289%2C5%29=x and log%2827%2C2%29=y, express log%283%2C100%29 in terms of x and y
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
log%289%2C5%29=x
9%5Ex=5
%283%5E2%29%5Ex=5
3%5E%282x%29=5
-
log%2827%2C2%29=y
%283%5E3%29%5Ey=2
3%5E%283y%29=2
-
Take log of each side for each, and find x and y from those.
-
Should be found system%28x=%281%2F2%29log%283%2C5%29%2Cand%2Cy=%281%2F3%29log%283%2C2%29%29.


The Question: log%283%2C100%29
log%283%2C2%5E2%29%2Blog%283%2C5%5E2%29
2%2Alog%283%2C2%29%2B2%2Alog%283%2C5%29
2%2A3y%2B2%2A2x
highlight%284x%2B6y%29

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


9%5Ex+=+%283%5E2%29%5Ex+=+3%5E%282x%29, so log%289%2C5%29=x --> log%283%2C5%29=2x

27%5Ey+=+%283%5E3%29%5Ey+=+3%5E%283y%29, so log%2827%2C2%29=y --> log%283%2C2%29+=+3y

Then