What is the domain of f(x,y)=(5x)/(ln(x^2-4)) ?

The domain of f(x,y)=(5x)/(ln(x^2-4)) is x sqrt(5)

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domain of f(x,y)=(5x)/(ln(x^2-4))

domain

f (x, y) = \frac{5 x}{ln ( x ^{2} - 4 )}

x < - 5 or - 5 < x < - 2 or 2 < x < 5 or x > 5

Interval Notation

(- \infty, - 5) \cup (- 5, - 2) \cup (2, 5) \cup (5, \infty)

Solution steps

Find positive values for logs:

x < - 2 or x > 2

Find undefined (singularity) points:

x = 5, x = - 5

Combine real regions and undefined points for final function domain

x < - 5 or - 5 < x < - 2 or 2 < x < 5 or x > 5

4 x - 5

y = 4 x + 3

f (x) = 2 (3)^{x}

0.001 x

7 x + 5 y = 12

What is the domain of f(x,y)=(5x)/(ln(x^2-4)) ?
The domain of f(x,y)=(5x)/(ln(x^2-4)) is x<-sqrt(5)\lor-sqrt(5)<x<-2\lor 2<x<sqrt(5)\lor x>sqrt(5)