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To convert the equation \( 10^{-2} = 0.01 \) to its logarithmic form, we apply the logarithmic definition. The general rule for converting an exponential equation to logarithmic form is:

\[
a^b = c \quad \text{is equivalent to} \quad \log_a(c) = b
\]

In your case:
- The base \( a \) is 10.
- The exponent \( b \) is \(-2\).
- The result \( c \) is \(0.01\).

So, the logarithmic form of the equation \( 10^{-2} = 0.01 \) is:

\[
\log_{10}(0.01) = -2
\]

Would you like further details on logarithmic transformations or examples?

Here are 5 related questions to further explore the concept:

1. How do you convert a general logarithmic equation back into exponential form?
2. What are the properties of logarithms that simplify complex expressions?
3. What is the logarithmic value of 1 for any base? Why is it special?
4. How can you solve logarithmic equations with unknown variables?
5. What is the relationship between natural logarithms and common logarithms?

**Tip**: Logarithms with a base of 10 are called common logarithms and are often used in scientific calculations due to their convenience with powers of 10.

Convert to Logarithmic Form: 10^{-2} = 0.01

Learn how to convert the exponential equation 10^{-2} = 0.01 into its logarithmic form. This example demonstrates key concepts in logarithms and exponents, making it perfect for students in Grades 8-10.

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