Problem

$\log _{3}(19)=$

Answer

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Answer

Final Answer: \(\boxed{2.680143859246375}\)

Steps

Step 1 ：To solve this problem, we need to calculate the logarithm base 3 of 19. This can be done using the formula: \(\log_b(a) = \frac{\log_c(a)}{\log_c(b)}\), where c can be any positive number. So, to calculate \(\log_3(19)\), we can use the formula: \(\log_3(19) = \frac{\log_e(19)}{\log_e(3)}\).

Step 2 ：Using this formula, we find that \(\log_3(19) = 2.680143859246375\).

Step 3 ：Final Answer: \(\boxed{2.680143859246375}\)

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