Question

the function f(x)=ln(x-13) is discontinuous at a=13

what given point would the function not be defined?

Answer 1

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Answer 2

ln is undefined in the Real numbers when its argument is negative. x-13<0
if x<13 f(x) is undefined. The reason for this is that e^x is always > 0

Answer 3

So the natural log of e has to be greater than 0 in order for the x<13 to be undefined?

is this in all cases or when a value is negative?

Answer 4

ln(13) means e to what power is 13. This has a solution.
ln(-3) means e to what power is -3. This is impossible in real numbers. so
ln(something) the something must be positive for the function to be defined in real numbers.

Answer 5

so in your case the something is x-13. we need it to be positive if it is defined. it is not defined when:
x-13<0
x<13