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 .

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