What is the value of logb(B)?

The value of logb(B) represents the logarithm of B with base b. By the definition of logarithms, logb(B) answers the question: "To what power must the base b be raised to produce B?"

In this case, when the base b is the same as the number B itself, it is clear that b raised to the power of 1 equals B (since b^1 = b). Therefore, logb(B) equals 1.

This understanding is fundamental in logarithmic functions, where the logarithm of a number with the same base always equals 1. This is why the correct answer is 1. A logarithm can also be thought of as the inverse operation of exponentiation, reinforcing this point because b raised to the power of 1 must yield B when the base corresponds exactly to that number.