What is the domain of f(x)= 1/(ln(5x+10)) ?

The domain of f(x)= 1/(ln(5x+10)) is -2 -9/5

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domain of f(x)= 1/(ln(5x+10))

domain

f (x) = \frac{1}{ln ( 5 x + 10 )}

- 2 < x < - \frac{9}{5} or x > - \frac{9}{5}

Interval Notation

(- 2, - \frac{9}{5}) \cup (- \frac{9}{5}, \infty)

Solution steps

Find positive values for logs:

x > - 2

Find undefined (singularity) points:

x = - \frac{9}{5}

Combine real regions and undefined points for final function domain

- 2 < x < - \frac{9}{5} or x > - \frac{9}{5}

y = \frac{x ^{2} - 25}{x ^{2}}

f (x) = arccos (\frac{- x}{2}) + \frac{π}{2}

\frac{- 16 + x}{4}

\frac{5}{3 x - 1}

f (x) = \frac{1}{0.5 arctan ( x )}

What is the domain of f(x)= 1/(ln(5x+10)) ?
The domain of f(x)= 1/(ln(5x+10)) is -2<x<-9/5 \lor x>-9/5