use change of base formula to evaluate logaritm for following and show work

logbase8 22



To evaluate \(\log_8 22\) using the change of base formula, we follow these steps.

### Change of Base Formula:
The change of base formula for logarithms states that:

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

Where:
- \( a \) is the number you are taking the logarithm of,
- \( b \) is the base,
- \( c \) is any base you choose (typically 10 or \( e \)).

For this case, we will use base 10 (common logarithm) to evaluate \(\log_8 22\).

\[
\log_8 22 = \frac{\log_{10} 22}{\log_{10} 8}
\]

Now let's evaluate both \(\log_{10} 22\) and \(\log_{10} 8\) using a calculator.

1. \(\log_{10} 22 \approx 1.3424\)
2. \(\log_{10} 8 \approx 0.9031\)

Now substitute these values into the change of base formula:

\[
\log_8 22 = \frac{1.3424}{0.9031} \approx 1.486
\]

### Final Answer:
\[
\log_8 22 \approx 1.486
\]

Would you like further details on any part of the solution?

Here are 5 related questions:
1. How would you evaluate \(\log_5 50\) using the change of base formula?
2. Can the change of base formula be applied to any logarithmic base?
3. What is the value of \(\log_8 64\)?
4. How can we express \(\log_8 22\) in terms of natural logarithms?
5. Why is the change of base formula useful in logarithmic calculations?

**Tip**: The change of base formula is especially helpful when calculating logarithms with uncommon bases, as most calculators only provide logarithms for base 10 and base \(e\).

use change of base formula to evaluate logaritm for following and show work logbase8 22

Learn how to evaluate log_8(22) using the change of base formula with a detailed step-by-step explanation. This problem covers logarithms and the change of base formula, making it suitable for students in Grades 9-12.

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