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

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) (Show Source): You can put this solution on YOUR website!
Solve for x:
Apply the product rule for logarithms:
Simplifying this, we get:
Now write this in exponential form: means Applying this to your problem:

Subtract 1000 from both sides.
Divide both sides by 100 to simplify this a bit.
Factor this quadratic equation.
Apply the principle of zero products:
or , so...
or Discard the negative solution as the log of a negative quantity results in a complex answer.
Your solution is:

Check:
=
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