What is the domain of f(x)=ln(((x-1))/((x-2))) ?

The domain of f(x)=ln(((x-1))/((x-2))) is x 2

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domain of f(x)=ln(((x-1))/((x-2)))

domain

f (x) = ln (\frac{( x - 1 )}{( x - 2 )})

x < 1 or x > 2

Interval Notation

(- \infty, 1) \cup (2, \infty)

Solution steps

Find positive values for logs:

x < 1 or x > 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x < 1 or x > 2

q (x) = \frac{x - 3}{x ^{2} + x - 12}

\frac{x ^{2} - 4 x + 4}{x ^{4} - 8 x ^{2} + 16}

f (x) = 10 - 9 x

f (x) = - \frac{12}{2 x - 9}

f (x) = - 3 (x^{2} + 5)

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