SOLUTION: Can you please help. Because these are not perfect squares, I can't figure them it. log3(x-5)+log3(x+3)=4. Thanks.

Question 195566This question is from textbook
: Can you please help. Because these are not perfect squares, I can't figure them it.
log3(x-5)+log3(x+3)=4. Thanks. This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Combine the logs using the identity

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

Raise 3 to the 4th power to get 81

FOIL

Subtract 81 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 .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the expression.

So the possible answers are or

However, since you cannot take the log of a negative number, this rules out

So the only solution is
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