Graph of y = ln(x)
Interactive graph of y = ln(x) (natural logarithm). Explore logarithmic growth, its inverse relationship to e^x, and key properties.
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Understanding the Function
The natural logarithm y = ln(x) is the inverse of the exponential function e^x. Its graph passes through (1, 0) and increases without bound, but extremely slowly compared to polynomial or exponential functions. It is undefined for x <= 0 and has a vertical asymptote at x = 0.
Logarithms convert multiplication into addition: ln(ab) = ln(a) + ln(b). This property made them indispensable for computation before electronic calculators and remains fundamental in information theory (entropy), acoustics (decibels), earthquake measurement (Richter scale), and algorithm analysis (O(log n) complexity).
Key properties: domain (0, infinity), range all real numbers, x-intercept at (1, 0), vertical asymptote at x = 0, derivative is 1/x, always increasing, always concave down. Note that in mathjs, log(x) computes the natural logarithm (base e).