Use the product property of logarithms, .

Apply the distributive property.

Simplify the expression.

Multiply by .

Multiply by .

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

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

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 .

Add to 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 .

Exclude the solutions that do not make true.

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