if `log_(m)n =rho`, then:

Options

A. `m^(n) = p`
B. `p^(n) =m`
C. `m^(p)=n`
D. `n^(p) =m`

Answer

To solve the problem where we have \( \log_m n = \rho \), we need to express this logarithmic equation in its exponential form.

### Step-by-Step Solution:

1. **Understanding the Logarithmic Equation**:
We start with the equation given:
\[ \log_m n = \rho \]
This means that \( n \) is the result of raising \( m \) to the power of \( \rho \).

2. **Converting to Exponential Form**:
To convert the logarithmic equation to its equivalent exponential form, we use the definition of logarithms:
\[ n = m^{\rho} \]

### Final Result:
Thus, if \( \log_m n = \rho \), then we can conclude that:
\[ n = m^{\rho} \]