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

Solve for x log base 5 of x-5+ log base 5 of x+15=3
Clarify the left side.
Use the product property of logarithms, .
Expand using the FOIL Method.
Use the distributive law.
Apply the distributive property.
Apply the distributive property.
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 .
Calculate
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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