# Solve for x log base six of x plus log base six of x minus three equals two

Use the product property of logarithms, .

Apply the distributive property.

Simplify the expression.

Multiply by .

Move to the left of .

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.

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify.

Simplify the numerator.

Raise to the power of .

Multiply by .

Multiply by .

Add and .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply by .

The final answer is the combination of both solutions.

Exclude the solutions that do not make true.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Do you need help with solving Solve for x log base 6 of x+ log base 6 of x-3=2? We can help you. You can write to our math experts in our application. The best solution for you is above on this page.