To solve the expression [tex]\(5 \log 6 - 7 \log 9.42 + 23 \log 34.5 - \log 10.5\)[/tex], follow these steps:
1. Calculate Each Logarithmic Term:
- First, compute [tex]\(5 \log 6\)[/tex]:
[tex]\[
5 \log 6 \approx 3.8908
\][/tex]
- Next, compute [tex]\(7 \log 9.42\)[/tex]:
[tex]\[
7 \log 9.42 \approx 6.8184
\][/tex]
- Then, compute [tex]\(23 \log 34.5\)[/tex]:
[tex]\[
23 \log 34.5 \approx 35.3698
\][/tex]
- Finally, compute [tex]\(\log 10.5\)[/tex]:
[tex]\[
\log 10.5 \approx 1.0212
\][/tex]
2. Combine the Terms Using Arithmetic Operations:
- Begin with the first term, subtract the second term:
[tex]\[
3.8908 - 6.8184 = -2.9276
\][/tex]
- Add the third term:
[tex]\[
-2.9276 + 35.3698 = 32.4422
\][/tex]
- Subtract the fourth term:
[tex]\[
32.4422 - 1.0212 = 31.4210
\][/tex]
3. Present the Final Result:
[tex]\[
5 \log 6 - 7 \log 9.42 + 23 \log 34.5 - \log 10.5 \approx 31.4210
\][/tex]
So, the detailed solution indicates that the final result of the given expression is approximately [tex]\(31.4210\)[/tex].
