Use the quotient property of logarithms, .

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

Multiply each term by and simplify.

Multiply each term in by .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify .

Apply the distributive property.

Multiply by .

Move all terms containing to the left side of the equation.

Subtract from both sides of the equation.

Subtract from .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Solve for x log of 2+x- log of x-2 = log of 3