Questions: log5(1)

Solution Steps

To solve the logarithm $\log_{5}(1)$, we need to determine the power to which the base 5 must be raised to get the number 1. By definition, any number raised to the power of 0 is 1. Therefore, $\log_{5}(1) = 0$.

We need to evaluate the expression \( \log_{5}(1) \). By the definition of logarithms, \( \log_{b}(a) = c \) means that \( b^c = a \). In this case, we are looking for \( c \) such that \( 5^c = 1 \).

We know that any non-zero number raised to the power of 0 equals 1. Therefore, we can conclude that: \[ 5^0 = 1 \] This implies that \( c = 0 \).

Thus, we find that: \[ \log_{5}(1) = 0 \]

Final Answer