SOLUTION: Can you please help me solve this? This is what I have so far. log5(x+3)+log5(x-3)=3 log5{(x+3)(x-3)}=3 (x+3)(x-3)=3^5 x^2-9=243 How do I finish this?

Question 167780: Can you please help me solve this? This is what I have so far.
log5(x+3)+log5(x-3)=3
log5{(x+3)(x-3)}=3
(x+3)(x-3)=3^5
x^2-9=243
How do I finish this?

Found 3 solutions by stanbon, Alan3354, jim_thompson5910:
Answer by stanbon(48535)   (Show Source):
You can put this solution on YOUR website!
log5(x+3)+log5(x-3)=3
log5{(x+3)(x-3)}=3
x^2-9 = 5^3
x^2 = 134
x = sqrt(134) or x= -sqrt(134)
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Cheers,
Stan H.

Answer by Alan3354(21583)   (Show Source):
You can put this solution on YOUR website!
Can you please help me solve this? This is what I have so far.
log5(x+3)+log5(x-3)=3
log5{(x+3)(x-3)}=3
(x+3)(x-3)=3^5 It's the base to the exponent.
x^2-9=243
How do I finish this?
------------------
log5(x+3)+log5(x-3)=3 I assume this is where you started.
Raise 5 to the power of each term. The 2 terms added are multiplied, since the logs are added.
(x-3)*(x+3) = 5^3 = 125
x^2-9 = 125
x^2 = 134
x = ± sqrt(134) = apx ± 11.576

Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
You're doing great. However, the third step should be (note the switch on the right side) which makes the fourth step

Note: remember, if , then . So the base of the log should be the base of the exponential expression

Start with the given equation

Add 9 to both sides.

Combine like terms.

Take the square root of both sides. Note: only the positive square root is considered since you CANNOT take the log of a negative number.

So the solution is