If `log_(a)m = n`, express `a^(n-1)` in terms of a and m.

Answer

To solve the problem, we start with the given equation:

1. **Given Equation**:
\[ \log_a m = n \]

2. **Convert to Exponential Form**:
To express \( m \) in terms of \( a \) and \( n \), we convert the logarithmic equation to its exponential form. The definition of logarithm states that if \( \log_a m = n \), then:
\[ m = a^n \]

3. **Express \( a^{n-1} \)**:
We need to express \( a^{n-1} \) in terms of \( a \) and \( m \). We can rewrite \( a^{n-1} \) as:
\[ a^{n-1} = \frac{a^n}{a} \]

4. **Substitute \( a^n \)**:
From step 2, we know that \( a^n = m \). We substitute this into our expression:
\[ a^{n-1} = \frac{m}{a} \]

5. **Final Expression**:
Thus, we have expressed \( a^{n-1} \) in terms of \( a \) and \( m \):
\[ a^{n-1} = \frac{m}{a} \]

### Summary of Steps:
1. Start with the logarithmic equation.
2. Convert to exponential form to find \( m \).
3. Rewrite \( a^{n-1} \) in terms of \( a^n \).
4. Substitute \( m \) for \( a^n \).
5. Conclude with the final expression.