SOLUTION: I need help solving this logarithmic equation: log (x+9)=1-log x

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Question 21525: I need help solving this logarithmic equation:
log (x+9)=1-log x

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
log%28%28x%2B9%29%29+=+1+-+logx Add logx to both sides.
log%28%28x%2B9%29%29+%2B+logx+=+1 Simplify the left side. (loga+logb = log(ab))
log%28%28x%5E2%2B9x%29%29+=+1 Substitute log10 = 1
log%28%28x%5E2%2B9x%29%29+=+log10 If loga = logb then a = b.
x%5E2%2B9x+=+10 Subtract 10 from both sides.
x%5E2%2B9x-10+=+0 Solve by factoring.
%28x-1%29%28x%2B10%29+=+0 Apply the zero product principle.
%28x-1%29+=+0 and/or %28x%2B10%29+=+0
If x-1+=+0 then, x+=+1
If x%2B10+=+0 then, x+=+-10
You can check the solutions by substitution.