1. Let's start by understanding what the number $e \approx 2.7182818$ represents. 2. The number $e$ is the base of the natural logarithm, also called the Napierian logarithm. 3. The logarithm with base $b$ is defined as $\log_b(x)$, which answers the question: "To what power must we raise $b$ to get $x$?" 4. Since $e$ is the base of the natural logarithm, we have $\log_e(e) = 1$ because $e^1 = e$. 5. More generally, for any positive number $x$, the natural logarithm is written as $\ln(x)$, meaning $\log_e(x)$. 6. So if we write $e = b$, then $\log_b(e) = 1$ and $e^1 = e$. 7. This means $e$ is the unique positive number such that the logarithm base $e$ of $e$ equals 1. 8. In summary, $e$ is the base number for which $\log_b(e)$ returns 1 exactly when $b = e$.