What is the value of logb(1)?

The value of logb(1) is 0 because of the fundamental properties of logarithms. By definition, the logarithm logb(x) answers the question: "To what power must the base b be raised to obtain x?"

If we let logb(1) equal a, then we are looking for the value of a in the equation b^a = 1. The only exponent that satisfies this equation for any base b (where b is greater than 0 and b is not equal to 1) is 0, since any non-zero number raised to the power of 0 equals 1. Therefore, logb(1) equals 0, confirming that this is the correct answer.

Understanding this concept is crucial in studying logarithms, as it illustrates how logarithmic functions behave and how they can be used to simplify expressions in various mathematical contexts.