Solve the logarithmic equation.

log_{5}^{x} + log_{5}^{(x+2)} = log_{5}^{3}

**Solution:-**

Rewrite the left side of the equation as one logarithm, using the properties of logarithms.

log_{5}^{(x(x+2))} = log_{5}^{3}

Next, exponentiate both sides of the equation.

x(x+2) = 3

Now, solve for x. Use the Distributive Property.

x^{2} + 2x = 3

Set the equation equal to zero.

x^{2} + 2x -3 = 0

Solve the resulting quadratic equation. Use the Quadratic Formula.

x =

Remember that the domain of log_{m}x is all x > 0, so the answer must be greater than zero.

x =

=1