To solve the problem, we need to evaluate the logarithmic expression:
$ \log_{1250}{1250} $
1. Understanding the Logarithmic Identity:
There is a basic identity in logarithms:
$ \log_b{b} = 1 $
That is, the logarithm of a number to its own base is always equal to 1.
2. Applying the Identity:
Here, the base is 1250 and the argument is also 1250:
$ \log_{1250}{1250} = 1 $
Final Answer:
The value is $ {1} $
Consider two distinct positive numbers \( m, n \) with \( m > n \). Let \[ x = n^{\log_n m}, \quad y = m^{\log_m n}. \] The relation between \( x \) and \( y \) is -
If \[ \log_{p^{1/2}} y \times \log_{y^{1/2}} p = 16, \] then find the value of the given expression.