The problem asks to simplify the logarithmic expression $\log 8 + \log 5 - \log 0.5$ into a single logarithm.

1. Problem Description

The problem asks to simplify the logarithmic expression $\log 8 + \log 5 - \log 0.5$ into a single logarithm.

2. Solution Steps

We will use the following logarithmic properties:

$\log a + \log b = \log (a \times b)$

$\log a - \log b = \log (\frac{a}{b})$

First, we combine the first two terms using the addition property:

$\log 8 + \log 5 = \log (8 \times 5) = \log 40$

Now we have:

$\log 40 - \log 0.5$

Using the subtraction property:

$\log 40 - \log 0.5 = \log (\frac{40}{0.5}) = \log (\frac{40}{\frac{1}{2}}) = \log (40 \times 2) = \log 80$

3. Final Answer

$\log 80$