Answer:
[tex]\log_7(u^5v^8)[/tex]
Explanation:
To write the expression as a single logarithm, we will use the following properties
[tex]\begin{gathered} 5\log_7x=\log_7x^5 \\ \log_7x+\log_7y=\log_7(xy) \end{gathered}[/tex]
Using the first property, we get
[tex]5\log_7u+8\log_7v=\log_7u^5+\log_7v^8[/tex]
Then, we need to use the second property, so
[tex]5\log_7u+8\log_7v=\log_7(u^5v^8)[/tex]
Therefore, the answer is
[tex]\log_7(u^5v^8)[/tex]
