Use the quotient property of logarithms, .

Multiply by .

Combine and simplify the denominator.

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify.

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 .

To remove the radical on the left side of the equation, square both sides of the equation.

Simplify each side of the equation.

Simplify the left side of the equation.

Raise to the power of .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify .

Raise to the power of .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x log base 2 of 6x- log base 2 of square root of x=2