The logarithm functions on calculators are typically labeled as “log” for base 10 and “ln” for the natural logarithm, which uses base $e$.

Logarithms provide a way to express the exponent to which a given base must be raised to produce a specific number. For instance, in the expression $\log_{10}(100)$, the base is $10$, and the logarithm indicates the power to which $10$ must be raised to yield $100$. In this case, we find that $\log_{10}(100) = 2$ because $10^2 = 100$.

Most scientific calculators feature two primary logarithmic functions: “log” and “ln”. The “log” button corresponds to base 10 logarithms, commonly referred to as common logarithms. These logarithms are especially useful in various scientific and engineering applications. For example, to determine the logarithm of $1000$ to base $10$, you would press the “log” button, enter $1000$, and the calculator would display $3$, since $10^3 = 1000$.

The “ln” button represents the natural logarithm, which is based on the constant $e$ (approximately equal to $2.718$). Natural logarithms are extensively utilized in advanced mathematics, particularly in calculus and complex number theory. For example, to compute the natural logarithm of $7$, you would press the “ln” button and enter $7$, resulting in an approximate value of $1.9459$, since $e^{1.9459} \approx 7$.

Familiarity with these functions on your calculator is essential for solving a wide range of problems involving exponential growth, decay, and other phenomena that are modeled by logarithmic relationships.