What is the domain of f(x)=((x5^x))/(5^{(x+2))-6} ?

The domain of f(x)=((x5^x))/(5^{(x+2))-6} is x (ln(6))/(ln(5))-2

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domain of f(x)=((x5^x))/(5^{(x+2))-6}

domain

f (x) = \frac{( x 5 ^{x} )}{5 ^{(x + 2)} - 6}

x < \frac{ln ( 6 )}{ln ( 5 )} - 2 or x > \frac{ln ( 6 )}{ln ( 5 )} - 2

Interval Notation

(- \infty, \frac{ln ( 6 )}{ln ( 5 )} - 2) \cup (\frac{ln ( 6 )}{ln ( 5 )} - 2, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{ln ( 6 )}{ln ( 5 )} - 2

The function domain

x < \frac{ln ( 6 )}{ln ( 5 )} - 2 or x > \frac{ln ( 6 )}{ln ( 5 )} - 2

\frac{x}{ln ( x - 1 ) - 1}

f (x) = \frac{x + 1}{x ^{2} - 9 x + 8}

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

\frac{x + 5}{3}

f (x) = cos (x - 7) + 4

What is the domain of f(x)=((x5^x))/(5^{(x+2))-6} ?
The domain of f(x)=((x5^x))/(5^{(x+2))-6} is x<(ln(6))/(ln(5))-2\lor x>(ln(6))/(ln(5))-2