If you want to find the domain, you want to find the values of for which f(x) is defined.

Now, it is not clear whether ln (x-2) has 2nd power or (x-2) has 2nd power

In the first case, f(x) will not be defined for x less than and equal to 2

in the second case, f(x) will not be defined for x=2.

logx is defined if

x is greater than 0

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