We want to write the following expression
[tex]6\log_7u+5\log_7v[/tex]
as a single expression. To do that, first, we're going to use the following property
[tex]a\log_bx=\log_bx^a[/tex]
Applying this property in our expression, we can rewrite it as
[tex]6\operatorname{\log}_7u+5\operatorname{\log}_7v=\operatorname{\log}_7u^6+\operatorname{\log}_7v^5[/tex]
Then, using the following property
[tex]\log_ax+\log_ay=\log_a(x\cdot y)[/tex]
we can rewrite our expression as
[tex]\operatorname{\log}_7u^6+\operatorname{\log}_7v^5=\operatorname{\log}_7u^6v^5[/tex]
