SOLUTION: Solve the paired simultaneous equation logx (base 2) + logy (base 2) = log36 (base 2) logx (base 2) - logy (base 2) = log 9 (base 2) if you can please show the working.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the paired simultaneous equation logx (base 2) + logy (base 2) = log36 (base 2) logx (base 2) - logy (base 2) = log 9 (base 2) if you can please show the working.       Log On


   

Question 917043: Solve the paired simultaneous equation
logx (base 2) + logy (base 2) = log36 (base 2)
logx (base 2) - logy (base 2) = log 9 (base 2)
if you can please show the working.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2Cx%29+%2B+log+%282%2Cy%29+=+log+%28+2%2C36%29 ..........eq.1
log%28+2%2Cx%29+-+log+%28+2%2Cy%29+=+log++%282%2C9%29+ .............eq.2
____________________________________________ add both

..........eq.1

2log%282%2Cx%29+=+log+%28+2%2C36%29%2Blog+%282%2C9%29
log%282%2Cx%5E2%29+=+log+%28+2%2C36%2A9%29+
log%282%2Cx%5E2%29+=+log+%28+2%2C324%29+ if log same, then
x%5E2+=+324+
x+=+sqrt%28324+%29
x+=+18 or x=-18
find y
if x=18
log%282%2C18%29+%2B+log+%282%2Cy%29+=+log+%28+2%2C36%29+ ..........eq.1
log+%282%2Cy%29+=+log%282%2C36%29-log%282%2C18%29
log+%282%2Cy%29+=+log+%28+2%2C36%2F18%29
log+%282%2Cy%29+=+log+%28+2%2C2%29 if log same, then
y=2
if+x=-18
log%282%2C-18%29+%2B+log+%282%2Cy%29+=+log+%28+2%2C36%29 ..........eq.1
log+%282%2Cy%29+=+log+%28+2%2C36%29-log%282%2C-18%29
log+%282%2Cy%29+=+log+%28+2%2C-36%2F18%29
log+%282%2Cy%29+=+log+%28+2%2C-2%29 if log same, then
y=-2