Question

sovle log3 x + log3 (x+2) = log3 8

Answer 1

but x = -4 does not work in the original equation, so must be discarded

Answer 2

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.

Answer 3

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.