The expression you're referring to is \( \log_3 43 \), which represents the logarithm of 43 with a base of 3. This value answers the question: "To what power must 3 be raised to obtain 43?"

Since 43 is not a power of 3, we can calculate this logarithm using the **change of base formula**:

\[
\log_b a = \frac{\log a}{\log b}
\]

Applying this formula for \( \log_3 43 \):

\[
\log_3 43 = \frac{\log 43}{\log 3}
\]

Using approximate values:

\[
\log 43 \approx 1.6335 \quad \text{and} \quad \log 3 \approx 0.4771
\]

\[
\log_3 43 \approx \frac{1.6335}{0.4771} \approx 3.424
\]

Thus, \( \log_3 43 \approx 3.424 \).

This means \( 3^{3.424} \) is approximately 43.

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

Here are 5 related questions:
1. How would you calculate \( \log_5 100 \) using the change of base formula?
2. Can you solve \( \log_3 x = 5 \) for \( x \)?
3. What is the general formula for converting a logarithm to a different base?
4. How do we evaluate \( \log_2 64 \) without a calculator?
5. What is the relationship between logarithms and exponents?

**Tip:** When working with logarithms, remember that they are the inverse of exponentiation.

Learn how to calculate the logarithm \( \log_3 43 \) using the change of base formula. This detailed solution explains step-by-step how to find the value, including an approximate calculation, and covers essential concepts in logarithms and exponents. Suitable for students in Grades 9-12.

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