SOLUTION: Use the properties of exponential and logarithmic functions to solve each system. {{{system(log(2,(x-2y)) = 3,log(2,(x+y)) = log(2,(8)))}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Use the properties of exponential and logarithmic functions to solve each system. {{{system(log(2,(x-2y)) = 3,log(2,(x+y)) = log(2,(8)))}}}       Log On


   

Question 1070042: Use the properties of exponential and logarithmic functions to solve each
system.
system%28log%282%2C%28x-2y%29%29+=+3%2Clog%282%2C%28x%2By%29%29+=+log%282%2C%288%29%29%29
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
system%28log%282%2C%28x-2y%29%29+=+3%2Clog%282%2C%28x%2By%29%29+=+log%282%2C%288%29%29%29

For the first equation, we use the definition of logarithm 
which states:

the logarithm equation log%28B%2CA%29=C is equivalent to
the exponential equation A=B%5EC  

The first equation log%282%2C%28x-2y%29%29+=+3 is equivalent to x-2y=2%5E3
and since 23=8, 

x-2y=8

For the second equation we use the principle:

If log%28B%2C%28P%29%29=log%28B%2C%28Q%29%29 then  P=Q

So the second equation becomes x%2By=8

So now we have the system of equations:

system%28x-2y=8%2Cx%2By=8%29

which you can solve by substitution or elimination/addition.

Answer:  (x,y) = (8,0)

Edwin