What is the domain of 1/((25)^x+4(5^x)-1) ?

The domain of 1/((25)^x+4(5^x)-1) is x (ln(-2+sqrt(5)))/(ln(5))

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domain of 1/((25)^x+4(5^x)-1)

domain

\frac{1}{( 25 ) ^{x} + 4 ( 5 ^{x} ) - 1}

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

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

y = 3 (x + 7) (x + 3)

y = \frac{x - 1}{x ^{2} - x - 2}

x - 2 sin (x)

\frac{\frac{7 y ^{4}}{8}}{\frac{5 y ^{6}}{3}}

g (x) = 5 x + 10

What is the domain of 1/((25)^x+4(5^x)-1) ?
The domain of 1/((25)^x+4(5^x)-1) is x<(ln(-2+sqrt(5)))/(ln(5))\lor x>(ln(-2+sqrt(5)))/(ln(5))