Solve the logarithmic equation.

Log x + log (x+2) = log 3

Solution

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

Log x *(x+2) = log 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 = $\frac{-2\pm \sqrt{16}}{2}$

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

x = $\frac{-2\pm \sqrt{16}}{2}$

= 1