To evaluate the expression \( \log 18 + \log 6 - \log 16^{\frac{1}{2}} \), we can use the properties of logarithms. Simplify \( \log 16^{\frac{1}{2}} \) Using the power rule of logarithms: \(\log 16^{\frac{1}{2}} = \frac{1}{2} \log 16\) Substitute back into the expression: Now rewrite the expression: \(\log 18 + \log 6 - \frac{1}{2} \log 16\) Combine the logarithms: Using the product property of logarithms: \(\log 18 + \log 6 = \log (18 \cdot 6) = \log 108\) So we can rewrite the expression as: \(\log 108 - \frac{1}{2} \log 16\) Rewrite \( \frac{1}{2} \log 16\) Using the power rule again: \(\frac{1}{2} \log 16 = \log 16^{\frac{1}{2}} = \log 4\) Substitute back; Now we have: \(\log 108 - \log 4\) Using the quotient property of logarithms: \(\log \left( \frac{108}{4} \right)\) Simplify \(\frac{108}{4}\) Calculating: \(\frac{108}{4}\) = 27 Thus, the expression simplifies to: log 27 = 3log3 NOTE: all is in base 10.