To find \( \log_4 35 \), we can use the given logarithm values and the property of logarithms \( \log_b(xy) = \log_b(x) + \log_b(y) \).
First, we can express 35 as follows:
\[ 35 = 7 \times 5 \]
Thus, we can write:
\[ \log_4 35 = \log_4 (7 \times 5) = \log_4 7 + \log_4 5 \]
Next, we need to find \( \log_4 5 \). We can express \( \log_4 5 \) using the change of base formula:
\[ \log_4 5 = \frac{\log_4 5^{1}}{1} = \frac{\log_4 5}{\log_4 4} = \frac{\log_4 5}{1} \]
Without directly knowing \( \log_4 5 \), we can also relate it to \( \log_4 7 \). We'll apply the change of base formula:
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Expressing \( \log_4 7 \) and \( \log_4 5 \):
- We have \( \log_4 7 \approx \log 7 / \log 4 \)
- We have \( \log_4 5 \approx \log 5 / \log 4 \)
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Now we can find \( \log_4 7 \) using the provided value of \( \log 7 \):
- \( \log_4 7 \approx 1.404 \)
- \( \log_4 5 \approx 1.161 \)
Now substituting the values into the equation:
\[ \log_4 35 \approx \log_4 7 + \log_4 5 = 1.404 + 1.161 \]
Calculating this yields:
\[ \log_4 35 \approx 1.404 + 1.161 \approx 2.565 \]
Therefore, the answer is:
2.565