What is the value of logb(1)?

The value of ( \log_b(1) ) can be understood through the definition of logarithms. The logarithm ( \log_b(x) ) answers the question: “To what power must ( b ) be raised to obtain ( x )?”

In the case of ( \log_b(1) ), we are asking: “To what power must ( b ) be raised to yield 1?” The answer to this is always 0, regardless of the base ( b ) (as long as ( b > 0 ) and ( b \neq 1 )). This is due to the fact that any non-zero number raised to the power of 0 equals 1.

Therefore, since ( b^0 = 1 ), it logically follows that ( \log_b(1) = 0 ). This understanding arises from the fundamental properties of exponents and logarithmic functions, making the value of ( \log_b(1) ) unambiguously zero.