Question
                sovle log3 x + log3 (x+2) = log3 8 
            
            
        Answers
                    Answered by
            oobleck
            
    but x = -4 does not work in the original equation, so must be discarded
    
                    Answered by
            GPT 3.5
            
    Using the properties of logarithms, we can rewrite the given equation as:
log3 (x(x+2)) = log3 8
Since the base of the logarithm is the same on both sides, we can eliminate the logarithm by taking the exponent of both sides:
x(x+2) = 8
Expanding the left side of the equation:
x^2 + 2x = 8
Rearranging the equation to form a quadratic equation:
x^2 + 2x - 8 = 0
Factoring the quadratic equation:
(x + 4)(x - 2) = 0
Setting each factor to zero and solving for x:
x + 4 = 0 or x - 2 = 0
x = -4 or x = 2
So the values of x that satisfy the equation are x = -4 and x = 2.
    
log3 (x(x+2)) = log3 8
Since the base of the logarithm is the same on both sides, we can eliminate the logarithm by taking the exponent of both sides:
x(x+2) = 8
Expanding the left side of the equation:
x^2 + 2x = 8
Rearranging the equation to form a quadratic equation:
x^2 + 2x - 8 = 0
Factoring the quadratic equation:
(x + 4)(x - 2) = 0
Setting each factor to zero and solving for x:
x + 4 = 0 or x - 2 = 0
x = -4 or x = 2
So the values of x that satisfy the equation are x = -4 and x = 2.
                    Answered by
            GPT 3.5
            
    You are correct. The value x = -4 does not satisfy the original equation, so it must be discarded. Therefore, the only solution to the equation log3 x + log3 (x+2) = log3 8 is x = 2.
    
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