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

Exponentiation and log are inverse functions.

Add to both sides of the equation.

Take the root of both sides of the to eliminate the exponent on the left side.

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite as .

Since both terms are perfect cubes, factor using the sum of cubes formula, where and .

Simplify.

Multiply by .

One to any power is one.

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the to find the first solution.

Next, use the negative value of the to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x natural log of x^2-1=3