To understand why the logarithm of \(0.6104^3\) is approximately \(0.7882\), we can start by applying the properties of logarithms. The relevant property states that:
\[ \log(a^b) = b \cdot \log(a) \]
In this case:
- \( a = 0.6104 \)
- \( b = 3 \)
Thus, we can express the logarithm as:
\[ \log(0.6104^3) = 3 \cdot \log(0.6104) \]
Now, if you have a logarithm table, you can check the value of \(\log(0.6104)\). Let's find an approximate value for \(\log(0.6104)\):
Assuming that:
\[ \log(0.6104) \approx -0.2148 \] (you would have to check your logarithm table for the exact value).
Then:
\[ \log(0.6104^3) = 3 \cdot (-0.2148) \approx -0.6444 \]
However, you mentioned that the logarithm table gives you a value of \(0.7882\). This appears to represent \(\log_{10}(x)\), where \( x \) is the actual logarithmic output you have when perhaps looking for a base such as \(10^{-0.6444}\).
If the value in your table is indeed \(0.7882\), then it might refer to something else or a specific logarithmic base that needs clarification. If you were looking up logarithms directly, double-check whether the values you've used pertain to powers of ten or not, ensuring you're interpreting \( \log \) correctly with regard to your base and your tables.
Let's conclude by noting that for \( \log(0.6104^3) \) itself, it accurately computes to a negative value based on standard logarithmic properties unless otherwise specified.