Expand the logarithm. Assume when necessary that all logarithmic quantities are defined. \( \log _{2}\left(\frac{53}{x^{2}+4}\right)=\square \)

To expand the logarithm, you can use the properties of logarithms. Specifically, you can apply the quotient rule, which states that the logarithm of a quotient is the difference of the logarithms. Therefore: \[ \log_{2}\left(\frac{53}{x^{2}+4}\right) = \log_{2}(53) - \log_{2}(x^{2}+4) \] This expansion separates the numerator and denominator, making it easier to work with each part individually if necessary!