Question

Expand the expression log(8x5)
log
⁡
(
8
𝑥
5
)
using the properties of logarithms.(1 point)
Responses

8logx−log5
8
log
⁡
𝑥
−
log
⁡
5
8logx−log5
8
log
⁡
𝑥
−
log
⁡
5

log8+logx
log
⁡
8
+
log
⁡
𝑥
log8+logx
log
⁡
8
+
log
⁡
𝑥

log8−logxlog5
log
⁡
8
−
log
⁡
𝑥
log
⁡
5
log8−logxlog5
log
⁡
8
−
log
⁡
𝑥
log
⁡
5

log8+logx−log5

Answer 1

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

1. **Product Property**: \( \log(ab) = \log a + \log b \)
2. **Power Property**: \( \log(a^b) = b \cdot \log a \)

Now, we can apply these properties step by step:

1. First, apply the Product Property:
\[
\log(8x^5) = \log(8) + \log(x^5)
\]

2. Next, apply the Power Property to \( \log(x^5) \):
\[
\log(x^5) = 5 \cdot \log(x)
\]

3. Putting it all together:
\[
\log(8x^5) = \log(8) + 5 \cdot \log(x)
\]

Thus, the expanded expression is:
\[
\log(8) + 5 \log(x)
\]

From the options you provided, none exactly matches this expression. However, the correct answer corresponding to the choices may not be clear without further context.

The correct expanded form is:
\[
\log(8) + 5\log(x)
\]