Question
sovle log3 x + log3 (x+2) = log3 8
Answers
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.
oobleck
but x = -4 does not work in the original equation, so must be discarded
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.