To rewrite the function \( f(x) = \log(x^{100} - 110) \) using the properties of logarithms, we need to recognize that this expression is already in a logarithmic form. However, we can simplify it further if we separate the logarithm of a product or quotient if applicable:
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First, notice that \( f(x) \) does not lend itself directly to standard logarithmic properties like the product or quotient rules since it contains a subtraction inside the logarithm.
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However, if we assume \( x^{100} \) is significantly larger than 110 for large values of \( x \), the expression can be approximated, but it's important to note that this is not technically rewriting using properties of logarithms.
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Ultimately, if you simply want to factor out whatever can be made simpler, unfortunately, you cannot split \( \log(a - b) \) unless \( b \) can be expressed as \( a \) in another form, which is not possible here.
Thus, the most we can do without departing from strict logarithmic properties seems to be leaving it as is:
\[ f(x) = \log(x^{100} - 110) \]
No further simplification using the properties of logarithms applies directly here. If the function \( f(x) \) is meant to be analyzed in terms of limits or approximate behaviors, that's a different approach, but it won't change the basic logarithmic structure.