What is the domain of f(x)=(sqrt(25-x^2))/(ln(2x-3)) ?

The domain of f(x)=(sqrt(25-x^2))/(ln(2x-3)) is 3/2 <x<2\lor 2<x<= 5

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domain of f(x)=(sqrt(25-x^2))/(ln(2x-3))

domain

f (x) = \frac{25 - x ^{2}}{ln ( 2 x - 3 )}

\frac{3}{2} < x < 2 or 2 < x \leq 5

Interval Notation

(\frac{3}{2}, 2) \cup (2, 5]

Solution steps

Find non-negative values for radicals:

- 5 \leq x \leq 5

Find positive values for logs:

x > \frac{3}{2}

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

\frac{3}{2} < x < 2 or 2 < x \leq 5

What is the domain of f(x)=(sqrt(25-x^2))/(ln(2x-3)) ?
The domain of f(x)=(sqrt(25-x^2))/(ln(2x-3)) is 3/2 <x<2\lor 2<x<= 5