1 Answer

Roggie · Answer 1 · 2023-10-25T14:40:20+0000

We want to write the following expression

$6\log_7u+5\log_7v$

as a single expression. To do that, first, we're going to use the following property

$a\log_bx=\log_bx^a$

Applying this property in our expression, we can rewrite it as

$6\operatorname{\log}_7u+5\operatorname{\log}_7v=\operatorname{\log}_7u^6+\operatorname{\log}_7v^5$

Then, using the following property

$\log_ax+\log_ay=\log_a(x\cdot y)$

we can rewrite our expression as

$\operatorname{\log}_7u^6+\operatorname{\log}_7v^5=\operatorname{\log}_7u^6v^5$

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