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} $
The product of all solutions of the equation \(e^{5(\log_e x)^2 + 3 = x^8, x > 0}\) , is :