Log3(5-x)+log3(-1-x)= --3

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To solve this logarithmic equation, we can use the properties of logarithms to combine the two logarithms on the left side of the equation.

First, recall that log a + log b = log ab.

Using this property, we can rewrite the left side of the equation as a single logarithm:

log3((5-x)(-1-x))

Next, simplify the expression within the logarithm:

(5-x)(-1-x) = -5 + x + x - x^2 = -5 - x - x^2

Therefore, the left side of the equation simplifies to:

log3(-5 - x - x^2)

Now, set this equal to -3:

log3(-5 - x - x^2) = -3

To solve for x, we need to exponentiate both sides with base 3:

3^log3(-5 - x - x^2) = 3^(-3)

This simplifies to:

-5 - x - x^2 = 1/27

Rearranging the equation, we get a quadratic equation:

x^2 + x + 5 + 1/27 = 0

Solving this quadratic equation will give us the possible values of x. We could use the quadratic formula or factoring to find the solutions for x.