We can factorize the expression inside the logarithm as follows:
$x^{2}-3 x-10 = (x-5)(x+2)$.
Step 2:
Substitute this factorization back into the function:
$f(x)=\log _{2 x-5}\left((x-5)(x+2)\right)$.
Step 3:
We can rewrite this as:
$f(x)=\log _{2 x-5}(x-5) +
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