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Fill in the missing values to make the equations true.

The missing value in the equation is \( 5 \), making the equation:

\[
\log_3 \left(\frac{1}{25}\right) = -2 \log_3 5
\]

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Here are 5 related questions you could explore:

1. How do logarithmic properties help solve this equation?
2. What does the negative sign in front of the logarithm signify in terms of transformations?
3. How would you solve a similar equation with a different base, such as \(\log_2\)?
4. Can you convert the equation into an exponential form to verify the solution?
5. What is the significance of \(\log_3(5)\) in other types of logarithmic problems?

**Tip**: Remember that \(\log_b(x^n)\) simplifies to \(n \log_b(x)\), which is key for solving equations like these.

Fill in the missing values to make the equation true: log_3(1/25) = -2 log_3(?)

Learn how to solve the logarithmic equation log_3(1/25) = -2 log_3(x). This problem uses key logarithmic properties such as the power and reciprocal rules. Suitable for students in Grades 9-11.

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