z=sqrt(x^(2)+y^(2)-4)+ln(×y)

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Evaluate Expression: To solve for z, we need to evaluate the expression given by z = sqrt(x^2 + y^2 - 4) + ln(xy). We will start by simplifying the square root and the natural logarithm separately.Simplify Square Root: First, let's consider the square root part: sqrt(x^2 + y^2 - 4). This expression represents the distance from the origin to the point (x, y) in a Cartesian plane, with a correction of -4 inside the square root. We cannot simplify this further without specific values for x and y.Simplify Natural Logarithm: Next, we look at the natural logarithm part: ln(xy). The natural logarithm of a product is the sum of the logarithms of the individual factors, so ln(xy) = ln(x) + ln(y). However, we cannot simplify this further without specific values for x and y.Combine Parts: Now, we combine the two parts we have evaluated: sqrt(x^2 + y^2 - 4) and ln(xy). The expression for z is simply the sum of these two parts, which cannot be simplified further algebraically.Consider Domain: We must also consider the domain of the function for z. The expression inside the square root, x^2 + y^2 - 4, must be greater than or equal to 0 for the square root to be real. Additionally, the product xy must be positive for the natural logarithm to be real, since the logarithm of a non-positive number is undefined.

$z=\sqrt{x^{2}+y^{2}-4}+\ln(xy)$

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z=x2+y2−4+ln⁡(xy)z=\sqrt{x^{2}+y^{2}-4}+\ln(xy)z=x2+y2−4​+ln(xy)

$z=\sqrt{x^{2}+y^{2}-4}+\ln(xy)$