Mock AIME 4 2006-2007 Problems/Problem 2

Problem

Two points $A(x_1, y_1)$ and $B(x_2, y_2)$ are chosen on the graph of $f(x) = \ln x$ , with $0 < x_1 < x_2$ . The points $C$ and $D$ trisect $\overline{AB}$ , with $AC < CB$ . Through $C$ a horizontal line is drawn to cut the curve at $E(x_3, y_3)$ . Find $x_3$ if $x_1 = 1$ and $x_2 = 1000$ .

Solution

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Mock AIME 4 2006-2007 Problems/Problem 2

Problem

Solution