Problem
[tex]\log ^x_{}\text{ - }\log ^2_{}\text{ + }\log ^y_{}\text{ - }\log ^5_{}[/tex]Concept
Apply addition and subtraction of logarithm.
[tex]\begin{gathered} \log ^m_{}\text{ - }\log ^n_{}=\log ^{\frac{m}{n}}_{^{}}\text{ } \\ \log ^m_{}\text{ + }\log ^n_{}\text{ = }\log ^{mn}_{^{}} \end{gathered}[/tex]Apply the theorem above to solve the question.
[tex]\begin{gathered} \log ^x_{^{}}\text{ - }\log ^2_{}\text{ + }\log ^y_{}\text{ - }\log ^5_{} \\ =\text{ }\log ^{\frac{x}{2}}_{}\text{ + }\log ^{\frac{y}{5}}_{} \\ \text{Multiply the power} \\ =\text{ }\log ^{\frac{x}{2}\text{ }\times\text{ }\frac{y}{5}}_{} \\ =\text{ }\log ^{\frac{xy}{10}}_{} \end{gathered}[/tex]Final answer
Option C
