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The solution to the equation \( 10^{x-3} = 202 \) is approximately \( x = 5.305 \). 

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Here are some related questions for you:
1. How do you solve equations involving logarithms?
2. What is the relationship between logarithms and exponents?
3. How would you handle a similar equation with a different base, such as \( 2^{x-3} = 202 \)?
4. How can logarithmic identities simplify solving such equations?
5. How do we interpret logarithmic scales in real-world applications?

**Tip:** When dealing with exponential equations, using logarithms can simplify the process of isolating the variable in the exponent!

Learn how to solve the exponential equation 10^(x-3) = 202 with a step-by-step explanation. This problem explores key algebraic concepts, including logarithmic transformations and properties. Suitable for high school students in Grades 9-12.

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