What is the domain of ln((2x-1)/(3x+1))+2 ?

The domain of ln((2x-1)/(3x+1))+2 is x 1/2

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domain of ln((2x-1)/(3x+1))+2

domain

ln (\frac{2 x - 1}{3 x + 1}) + 2

x < - \frac{1}{3} or x > \frac{1}{2}

Interval Notation

(- \infty, - \frac{1}{3}) \cup (\frac{1}{2}, \infty)

Solution steps

Find positive values for logs:

x < - \frac{1}{3} or x > \frac{1}{2}

Find undefined (singularity) points:

x = - \frac{1}{3}

Combine real regions and undefined points for final function domain

x < - \frac{1}{3} or x > \frac{1}{2}

\frac{x ^{2} - 1}{x ^{3} - 8}

\frac{\frac{5}{x}}{\frac{5}{x} + 2}

ln (x) + ln (9 - x)

ln (x^{2} + 2 x - 15) + e^{5 - 4 x}

What is the domain of ln((2x-1)/(3x+1))+2 ?
The domain of ln((2x-1)/(3x+1))+2 is x<-1/3 \lor x> 1/2