SOLUTION: A) if logbase4(xy)=6 then prove that logbase2(x) +logbase2(y) = 12 B) Hence solve the equations simultaneously: Logbase4 (xy) = 6 (Logbase2(X))(logbase2(y)) = 32

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: A) if logbase4(xy)=6 then prove that logbase2(x) +logbase2(y) = 12 B) Hence solve the equations simultaneously: Logbase4 (xy) = 6 (Logbase2(X))(logbase2(y)) = 32      Log On


   

Question 1043800: A) if logbase4(xy)=6 then prove that logbase2(x) +logbase2(y) = 12
B) Hence solve the equations simultaneously:
Logbase4 (xy) = 6
(Logbase2(X))(logbase2(y)) = 32
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
This is help only, for (A).

log%284%2Cxy%29=6, given condition.

Change-Of-Base formula gives log%284%2Cxy%29=log%282%2Cxy%29%2Flog%282%2C4%29=6
Continuing with the left side steps,
%28log%282%2Cx%29%2Blog%282%2Cy%29%29%2Flog%282%2C2%5E2%29
%28log%282%2Cx%29%2Blog%282%2Cy%29%29%2F%282%2Alog%282%2C2%29%29
%28log%282%2Cx%29%2Blog%282%2Cy%29%29%2F%282%2A1%29
%28log%282%2Cx%29%2Blog%282%2Cy%29%29%2F2=6%29