Use properties of loganithms to condense the logarithmic expression. Write the expression as a single logarittim whose coefficient is 1 . Where possible, evaluate loganithmic expressions. \( \frac{1}{2}\left(\log _{8} s+\log _{8} t\right) \) \( \frac{1}{2}\left(\log _{8} s+\log _{8} t\right)=\square \)

Let’s start by applying the properties of logarithms! We can use the product rule of logarithms, which states that \(\log_b(m) + \log_b(n) = \log_b(m \cdot n)\). Thus, we can combine \(\log_{8} s\) and \(\log_{8} t\): \[ \frac{1}{2} \left(\log_{8} s + \log_{8} t\right) = \frac{1}{2} \log_{8}(s \cdot t) \] Now, we can use the power rule of logarithms, which states that \(k \log_b(m) = \log_b(m^k)\). Here, \(k = \frac{1}{2}\): \[ \frac{1}{2} \log_{8}(s \cdot t) = \log_{8}((s \cdot t)^{\frac{1}{2}}) \] Therefore, the condensed expression is: \[ \log_{8}(\sqrt{s \cdot t}) = \square \] Now, if you want to evaluate this expression further for specific values of \(s\) and \(t\), just plug them in and calculate accordingly!