# Solve for x 2 log of 4- log of 3+2 log of x-4=0

Simplify the left side.
Simplify each term.
Simplify by moving inside the logarithm.
Raise to the power of .
Simplify by moving inside the logarithm.
Use the quotient property of logarithms, .
Use the product property of logarithms, .
Combine and .
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Solve for
Anything raised to is .
Rewrite the equation as .
Multiply both sides of the equation by .
Simplify both sides of the equation.
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Take the root of each side of the to set up the solution for
Remove the perfect root factor under the radical to solve for .
Simplify the right side of the equation.
Rewrite as .
Simplify the denominator.
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.
Add to both sides of the equation.
Next, use the negative value of the to find the second solution.
Add to both sides of the equation.
The complete solution is the result of both the positive and negative portions of the solution.
Exclude the solutions that do not make true.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Solve for x 2 log of 4- log of 3+2 log of x-4=0