Find the logarithm using the change of base formula.
log Subscript 3 Baseline 19
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Part 1
log Subscript 3 Baseline 19equals
  
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​(Round to four decimal places as​ needed.)

To find \( \log_3 19 \) using the change of base formula, we convert it to a base-10 (or base-\( e \)) logarithm. The change of base formula is:

\[
\log_3 19 = \frac{\log 19}{\log 3}
\]

1. Calculate \( \log 19 \) and \( \log 3 \):
   - \( \log 19 \approx 1.2788 \)
   - \( \log 3 \approx 0.4771 \)

2. Substitute these values into the formula:

\[
\log_3 19 \approx \frac{1.2788}{0.4771} \approx 2.6799
\]

Thus:

\[
\log_3 19 \approx 2.6799
\]

### Final Answer:
\[
\log_3 19 \approx 2.6799
\]

Would you like a more detailed breakdown or have any questions?

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**Related Questions:**

1. How does the change of base formula work for other logarithmic bases?
2. What is the natural logarithm \( \ln \) equivalent of \( \log_3 19 \)?
3. How would you find \( \log_5 50 \) using the same method?
4. Why is the change of base formula useful in logarithmic calculations?
5. What is the result of \( \log_3 19 \) using base-\( e \) instead of base-10?

**Tip:** Remember, using the change of base formula can simplify calculations when a calculator only provides \( \log \) (base-10) or \( \ln \) (base-\( e \)).

Find the logarithm using the change of base formula. log_3 19. (Round to four decimal places as needed.)

Find the logarithm of log_3 19 by using the change of base formula. This solution includes a step-by-step breakdown of the calculation, converting the base-3 logarithm to base-10, and rounding to four decimal places. Ideal for high school students studying logarithmic concepts.

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