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The given equation is:

\[
\log_{10} (x - a) = n
\]

To solve for \(x\), we need to eliminate the logarithm by rewriting it in exponential form. The general form of a logarithmic equation is:

\[
\log_b y = x \quad \text{implies} \quad y = b^x
\]

Here, the base \(b = 10\). Thus, we can rewrite the equation as:

\[
x - a = 10^n
\]

Finally, solving for \(x\) gives:

\[
x = 10^n + a
\]

This is the relationship for \(x\) in terms of \(n\) and \(a\).

Would you like more details or have any further questions? Here are 5 related questions to explore further:

1. How do we handle logarithms with different bases?
2. What is the inverse relationship between logarithms and exponentials?
3. How can you solve logarithmic equations with variables inside the logarithm?
4. What are some common properties of logarithms?
5. How would this equation change if the base of the logarithm was \(e\) (natural log)?

**Tip:** When dealing with logarithmic equations, always remember that the logarithm's base determines the exponent in the exponential form of the equation.

If log10(x - a) = n, then solving for x gives what relationship?

This problem involves solving a logarithmic equation log10(x - a) = n by converting it into its exponential form. Learn how to manipulate logarithmic functions and understand the relationship between x, n, and a. Suitable for students in Grades 9-12.

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