SOLUTION: Log3(1-x)=log3(x+16-x^2)

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Question 1156244: Log3(1-x)=log3(x+16-x^2)
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!

We can't tell whether you mean the 3's to be the base of the logarithm
like this:



or whether you mean the 3's to be multipliers and the logarithms understood
to be common logs with understood base 10, like this:

 

If it's the first way then we drop the logs and get this:



If it's the second way then we drop the logs and get this:



But if it's that way we divide both sides by 3 and get



So, luckily here it doesn't matter which you meant but in other
logarithm problems it would make a difference.  So be careful.



Get 0 on the right and descending order on the left:





    
       

But we must check in the original equation for extraneous solutions.

If it was the first way, we check to see if 5 is a solution:




It looks like it checks but it doesn't because logs cannot be taken of
negative numbers in real number mathematics.  So 5 is extraneous.

If it was the first way, we check to see if -3 is a solution:




That checks.  So x = -3 is the only solution.

If you meant the other way, it still would be only x = -3.

Edwin

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