Answer:
The value of the given expression is;
[tex]5[/tex]Explanation:
Given the logarithmic expression;
[tex]\log _416+\log _327[/tex]To solve, Recall the rules of logarithm;
[tex]\begin{gathered} \log _ax^y=y\times\log _ax\text{ ------1} \\ \log _aa=1\text{ -------2} \end{gathered}[/tex]Apply the above rules;
[tex]\begin{gathered} \log _416+\log _327 \\ \log _44^2+\log _33^3 \\ \text{Applying rule 1;} \\ 2\log _44+3\log _33 \end{gathered}[/tex]Aplplying rule 2;
[tex]\begin{gathered} 2\log _44+3\log _33 \\ =2(1)+3(1) \\ =2+3 \\ =5 \\ \log _416+\log _327=5 \end{gathered}[/tex][tex]\begin{gathered} \text{Note that from the rule 2;} \\ \log _aa=1 \\ so\text{ when a logarithm has the same number as the base it will equal to 1;} \\ \text{for example;} \\ \log _44=1 \\ \log _33=1 \\ \log _55=1 \end{gathered}[/tex]Therefore, the value of the given expression is;
[tex]5[/tex]