# Solve for x log base 5 of x+3=1- log base 5 of x+7 Move all the terms containing a logarithm to the left side of the equation.
Use the product property of logarithms, .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Move to the left of .
Multiply by .
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Solve for
Evaluate the exponent.
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.
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.
Set equal to and solve for .
Set the factor equal to .
Subtract from 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.
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