SOLUTION: Solve for x: log_12 (x-3) + log

SOLUTION: Solve for x: log_12 (x-3) + log_12 (x+1)=1

Question 177040: Solve for x: log_12 (x-3) + log_12 (x+1)=1
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Take note that (for the first log) and (for the second log). So the domain is (this interval works for both logs)

Note: remember, you cannot take the log of 0 or a negative number.

Combine the logs using the identity

Rewrite the equation using the property: ====>

Raise 12 to the first power to get 12

FOIL

Subtract 12 from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, since the value is NOT in the domain , this means that is NOT a valid solution.

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Answer:

So the only solution is
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