Question

Hello, I need help with this precalculus homework question, please?HW Q10

Answer 1

`\log_7(u^5v^8)`

Step-by-step explanation:

To write the expression as a single logarithm, we will use the following properties

`\begin{gathered} 5\log_7x=\log_7x^5 \\ \log_7x+\log_7y=\log_7(xy) \end{gathered}`

Using the first property, we get

`5\log_7u+8\log_7v=\log_7u^5+\log_7v^8`

Then, we need to use the second property, so

`5\log_7u+8\log_7v=\log_7(u^5v^8)`

Therefore, the answer is

`\log_7(u^5v^8)`