# Find the Domain natural log of 25-x^2-25y^2

Set the argument in greater than to find where the expression is defined.
Solve for .
Move all terms not containing to the right side of the inequality.
Subtract from both sides of the inequality.
Add to both sides of the inequality.
Multiply each term in by
Multiply each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Multiply .
Multiply by .
Multiply by .
Simplify each term.
Multiply by .
Multiply by .
Take the root of both sides of the to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical.
One to any power is one.
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution. Since this is an inequality, flip the direction of the inequality sign on the portion of the solution.
The complete solution is the result of both the positive and negative portions of the solution.
and
Find the intersection.
The domain is all real numbers.
Interval Notation:
Set-Builder Notation:
Find the Domain natural log of 25-x^2-25y^2