SOLUTION: log(2+x)-log(x)=log 11 could you help explain how to do this

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Question 21784: log(2+x)-log(x)=log 11 could you help explain how to do this
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
log%28%282%2Bx%29%29+-+log%28x%29+=+log%2811%29 Apply the Quotient rule for logarithms to the left side. log%28M%29+-+log%28N%29+=+log%28%28M%2FN%29%29
log%28%28%282%2Bx%29%2Fx%29%29+=+log%2811%29 If log a = log b, then a = b
%282%2Bx%29%2Fx+=+11 Multiply both sides by x.
2%2Bx+=+11x Subtract x from both sides.
2+=+10x Divide both sides by 10.
x+=+2%2F10
x+=+0.2
Check: Use your calculator or a table of logarithms to find the values of the logs.
log%28%282%2B0.2%29%29+-+log%280.2%29+=+1.04139
log%2811%29+=+1.04139