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Devonte used the change of base formula to approximate log8 25. Which expression did Devonte use?

To approximate \(\log_8{25}\), Devonte likely used the change of base formula, which is given by:

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

where \(a\) is the original base and \(b\) is the argument. The formula is valid for any positive base \(c\), but commonly, \(c\) is chosen to be either 10 (common logarithm) or \(e\) (natural logarithm).

In this case, to approximate \(\log_8{25}\), the change of base formula would be:

\[
\log_8{25} = \frac{\log{25}}{\log{8}}
\]

From the options in the image, the correct answer that Devonte would have used is:

\[
\frac{\log{25}}{\log{8}}
\]

This corresponds to the second option in the image.

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Would you like more details or have any questions? Here are some related questions:

1. How do you apply the change of base formula with natural logarithms?
2. What is the relationship between different logarithm bases?
3. Can you approximate \(\log_8{25}\) using the common logarithm values?
4. How does the change of base formula simplify calculations on calculators?
5. What are other methods to compute logarithms with non-standard bases?

**Tip:** When using a calculator, the change of base formula is particularly useful because most calculators only have buttons for \(\log_{10}\) and \(\ln\) (logarithm base \(e\)).

Devonte used the change of base formula to approximate log8 25. Which expression did Devonte use?

Discover how Devonte used the change of base formula to approximate log8 25. This problem covers essential logarithmic concepts and formulas suitable for students in Grades 9-12.

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