SOLUTION: if log4 in base 3 = x and log9 in base 4 = y, find the value of xy.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: if log4 in base 3 = x and log9 in base 4 = y, find the value of xy.       Log On


   

Question 1062570: if log4 in base 3 = x and log9 in base 4 = y, find the value of xy.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+4%2C9+%29+=+y+
+log%28+3%2C4+%29+=+x+
------------------
Writing the inverse:
(1) +4%5Ey+=+9+
(2) +3%5Ex+=+4+
-----------------
By substitution:
+%28+3%5Ex+%29%5Ey+=+9+
+3%5E%28x%2Ay%29+=+9+
+x%2Ay+=+2+
------------------
Maybe there is a way to prove the answer.
I don't know what that is.