# Solve for x log base 4 of x+3+ log base 4 of x-3=2

Simplify the left side.
Use the product property of logarithms, .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify terms.
Combine the opposite terms in .
Reorder the factors in the terms and .
Simplify each term.
Multiply by .
Multiply by .
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Solve for
Raise to the power of .
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
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 .
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 4 of x+3+ log base 4 of x-3=2