# Solve for x log base five of x minus five plus log base five of x plus fifteen equals three

Use the product property of logarithms, .

Expand using the FOIL Method.

Use the distributive law.

Apply the distributive property.

Apply the distributive property.

Clarify and Add like terms.

Clarify each term.

First, multiply by .

Move to the left of .

Multiply by .

Subtract from .

Should be rewritten 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.

Subtract from .

Factor using the AC method.

Use the form. Find a pair of integers whose product is and whose sum is . In such a case, whose product is and whose sum is .

Use the integers to write the factored form.

Set equal to and Calculate .

Make the factor equal .

Add to both sides of the equation.

Set equal to and Calculate .

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.

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