ThmDex – An index of mathematical definitions, results, and conjectures.

Value of standard logarithm function at its parameter value

Formulation 0

Let $\log_a$ be the D866: Standard real logarithm function in base $a \in (0, \infty) \setminus \{ 1 \}$.

Then \begin{equation} \log_a a = 1 \end{equation}

Proofs

Proof 0

Let $\log_a$ be the D866: Standard real logarithm function in base $a \in (0, \infty) \setminus \{ 1 \}$.

Directly from the definition, we have \begin{equation} \log_a a = \frac{\log_e a}{\log_e a} = 1 \end{equation} $\square$