Use the product property of logarithms, .

Apply the distributive property.

Simplify the expression.

Multiply by .

Move to the left of .

To solve for , rewrite the equation using properties of logarithms.

Exponentiation and log are inverse functions.

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

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify.

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Rewrite as .

Factor out of .

Factor out of .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply by .

Simplify .

The final answer is the combination of both solutions.

Exclude the solutions that do not make true.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x natural log of x+ natural log of x+2=4