SOLUTION: Can anyone tell me the correct answer to this prob?? log(x-9)+log 100x = 3?? I keep getting .12 but when I plug it back into the problem it doesn't work. Thanks so much for your

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Can anyone tell me the correct answer to this prob?? log(x-9)+log 100x = 3?? I keep getting .12 but when I plug it back into the problem it doesn't work. Thanks so much for your       Log On


   

Question 79561: Can anyone tell me the correct answer to this prob?? log(x-9)+log 100x = 3??
I keep getting .12 but when I plug it back into the problem it doesn't work. Thanks so much for your help.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
Log%5B10%5D%28x-9%29%2BLog%5B10%5D%28100x%29+=+3 Apply the product rule for logarithms:Log%5Bb%5D%28A%29%2BLog%5Bb%5D%28B%29+=+Log%5Bb%5D%28A%2AB%29
Log%5B10%5D%28%28x-9%29%2A%28100x%29%29+=+3 Simplifying this, we get:
Log%5B10%5D%28100x%5E2-900x%29+=+3 Now write this in exponential form: Log%5Bb%5D%28x%29+=+y meansb%5Ey+=+x Applying this to your problem:
10%5E3+=+100x%5E2-900x
1000+=+100x%5E2-900x Subtract 1000 from both sides.
100x%5E2-900x-1000+=+0 Divide both sides by 100 to simplify this a bit.
x%5E2-9x-10+=+0 Factor this quadratic equation.
%28x-10%29%28x%2B1%29+=+0 Apply the principle of zero products:
x-10+=+0 or x%2B1+=+0, so...
x+=+10 or x+=+-1 Discard the negative solution as the log of a negative quantity results in a complex answer.
Your solution is:
x+=+10
Check:
Log%2810-9%29%2BLog%2810%2A100%29+=+Log%281%29%2BLog%281000%29=0%2B3+=+3