The graph of ln x is a curve that starts from negative infinity on the left side and approaches positive infinity as x approaches infinity. The curve passes through the point (1, 0) and is asymptotic to the x-axis as x approaches zero. The graph is concave upward, meaning the rate of increase slows down as x increases, similar to the curve of square root function. The slope of the curve decreases as x increases, and the curve becomes flatter. The ln x graph has numerous applications in mathematics, science, and engineering, such as in calculus, statistics, thermodynamics, and quantum mechanics.
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