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The given problem is asking to solve for \( x \) in the equation:

\[
\log_{10} x = -2
\]

### Step-by-step Solution:

1. The definition of logarithms states that if \( \log_b a = c \), then \( a = b^c \).
   - In this case, \( b = 10 \), \( c = -2 \), and \( a = x \).
   - So, we can rewrite the equation as:
   \[
   x = 10^{-2}
   \]

2. Calculate \( 10^{-2} \):
   \[
   10^{-2} = \frac{1}{100}
   \]

Thus, the value of \( x \) is:

\[
x = \frac{1}{100}
\]

### Conclusion:
The correct answer is the first option:
\[
x = \frac{1}{100}
\]

Would you like more details on logarithmic functions or have any other questions?

Here are 5 related questions to expand on this topic:
1. What is the logarithmic rule for converting logs to exponents?
2. How do you solve logarithmic equations with different bases?
3. What is the inverse function of a logarithmic equation?
4. How would you handle a logarithmic equation with a variable in the base?
5. What happens if the logarithmic equation is \( \log_b x = -1 \)?

**Tip**: Logarithms are just another way to express powers! For example, \( \log_b x = y \) is the same as saying \( x = b^y \).

If log10(x) = -2, what is the value of x?

Learn how to solve the logarithmic equation log10(x) = -2. This problem explains key logarithmic concepts and exponential rules to find the value of x. Suitable for students in Grades 9-12.

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