Use the quotient property of logarithms, .

Factor out of .

Factor out of .

Raise to the power of .

Factor out of .

Factor out of .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .

Raise to the power of .

Rewrite the equation as .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

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 .

Pull terms out from under the radical, assuming positive real numbers.

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.

Exclude the solutions that do not make true.

Solve for x log base 7 of 3x^3+x- log base 7 of x=2