Expand the expression log(8x5) using the properties of logarithms.(1 point) Responses log8+logx log8+logx log8+logx−log5 log8+logx−log5 8logx−log5 8logx−log5 log8−logxlog5 log8−logxlog5

Answer 1

To expand the expression \(\log(8x^5)\) using the properties of logarithms, we can apply the following properties:

1. \(\log(ab) = \log a + \log b\)
2. \(\log(a^b) = b \cdot \log a\)

Using these properties, we can break down the expression step by step:

1. First, apply the product property of logarithms: \[ \log(8x^5) = \log(8) + \log(x^5) \]

2. Next, apply the power property of logarithms to \(\log(x^5)\): \[ \log(8) + \log(x^5) = \log(8) + 5 \cdot \log(x) \]

Putting it all together, we obtain: \[ \log(8x^5) = \log(8) + 5\log(x) \]

Now let's look at the options provided:

1. \(\log8 + \log x\)
2. \(\log8 + \log x\)
3. \(\log8 + \log x - \log5\)
4. \(8\log x - \log5\)
5. \(8\log x - \log5\)
6. \(\log8 - \log x \log5\)
7. \(\log8 - \log x \log5\)

The correct expression that matches our expansion is: \[ \log(8) + 5 \log(x) \]

However, none of the provided options seem to match our final answer. The closest formats are pack containing \(\log x\) and constants, but they are not equal to \(5\log x\). Ensure to double-check your provided options. If you need further clarifications or corrections, please provide the correct choices!