To find the result of the expression [tex]\(4 \log 8 + 4 \log 32\)[/tex], let's break it down:
1. Step 1: Simplify the expression using logarithm properties:
[tex]\[
4 \log 8 + 4 \log 32 = 4 (\log 8 + \log 32)
\][/tex]
2. Step 2: Use the logarithm addition property:
[tex]\[
\log 8 + \log 32 = \log(8 \cdot 32)
\][/tex]
3. Step 3: Simplify within the logarithm:
[tex]\[
8 \cdot 32 = 256
\][/tex]
Thus,
[tex]\[
\log 8 + \log 32 = \log 256
\][/tex]
4. Step 4: Substitute back into the expression:
[tex]\[
4 (\log 8 + \log 32) = 4 (\log 256)
\][/tex]
5. Step 5: Evaluate:
[tex]\[
4 \log 256
\][/tex]
Given that the evaluation of individual logarithms and the expression yields values:
[tex]\[
\log 8 \approx 0.9031, \quad \log 32 \approx 1.5051
\][/tex]
[tex]\[
4 \log 8 \approx 4 \times 0.9031 = 3.6124
\][/tex]
[tex]\[
4 \log 32 \approx 4 \times 1.5051 = 6.0206
\][/tex]
[tex]\[
4 \log 8 + 4 \log 32 \approx 3.6124 + 6.0206 = 9.63296
\][/tex]
Therefore, the result of [tex]\( 4 \log 8 + 4 \log 32 \)[/tex] is approximately [tex]\(\boxed{9.63296}\)[/tex].
