What is the domain of f(x)=((x5^x))/(5^{(x+2))-2} ?

The domain of f(x)=((x5^x))/(5^{(x+2))-2} is x (ln(2))/(ln(5))-2

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domain of f(x)=((x5^x))/(5^{(x+2))-2}

domain

x < \frac{ln ( 2 )}{ln ( 5 )} - 2 or x > \frac{ln ( 2 )}{ln ( 5 )} - 2

Interval Notation

(- \infty, \frac{ln ( 2 )}{ln ( 5 )} - 2) \cup (\frac{ln ( 2 )}{ln ( 5 )} - 2, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{ln ( 2 )}{ln ( 5 )} - 2

The function domain

x < \frac{ln ( 2 )}{ln ( 5 )} - 2 or x > \frac{ln ( 2 )}{ln ( 5 )} - 2

What is the domain of f(x)=((x5^x))/(5^{(x+2))-2} ?
The domain of f(x)=((x5^x))/(5^{(x+2))-2} is x<(ln(2))/(ln(5))-2\lor x>(ln(2))/(ln(5))-2