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

The domain of (5x)/(ln(x^2-4)) is x sqrt(5)

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domain of (5x)/(ln(x^2-4))

domain

\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

e x t re m e f (x) = - 0.3 x^{2} + 2.4 x + 98.6

sy mm e t ry y = \frac{x ^{9}}{81 - x ^{2}}

sy mm e t ry y = - x^{2} - 5

in v erse f (x) = \frac{x}{2}

r an g e f (x) = 9 x

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