# Solve for x log base 6 of 2x-6+ log base 6 of x=2

Simplify the left side.
Use the product property of logarithms, .
Apply the distributive property.
Multiply by by adding the exponents.
Move .
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 to the left side of the equation by subtracting it from both sides.
Factor the left side of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor.
Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Remove unnecessary parentheses.
Divide both sides of the equation by . Dividing by any non-zero number is .
Set equal to and solve for .
Set the factor equal to .
Add to both sides of the equation.
Set equal to and solve for .
Set the factor equal to .
Subtract from both sides of the equation.
The solution is the result of and .
Exclude the solutions that do not make true.
Solve for x log base 6 of 2x-6+ log base 6 of x=2