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.

Add to both sides of the equation.

Simplify the left side of the equation.

Simplify each term.

Rewrite as .

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 .

Move to the left of .

Rewrite as .

Rewrite as .

Multiply by .

Subtract from .

Add and .

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

Add and .

Factor using the AC method.

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

Set equal to and solve for .

Set the factor equal to .

Subtract from both sides of the equation.

Set equal to and solve for .

Set the factor equal to .

Subtract from both sides of the equation.

The solution is the result of and .

Solve for x log of (x-1)^2 = log of -5x-1