Move all the terms containing a logarithm to the left side of the equation.

Use the product property of logarithms, .

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify each term.

Multiply by .

Move to the left of .

Multiply by .

Add and .

Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .

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.

Solve for x log base 5 of x+3=1- log base 5 of x+7