Use the product property of logarithms, .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Subtract from .

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

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

Subtract from both sides of the equation.

Subtract from .

Move to the left side of the equation by adding it to both sides.

Add and .

Factor using the perfect square rule.

Rewrite as .

Check the middle term by multiplying and compare this result with the middle term in the original expression.

Simplify.

Factor using the perfect square trinomial rule , where and .

Set equal to and solve for .

Set the factor equal to .

Add to both sides of the equation.

The solution is the result of .

Exclude the solutions that do not make true.

No solution

Solve for x natural log of x-6+ natural log of x+1 = natural log of x-15