WEBVTT

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Here is the problem: e to the power 2x minus 3e to the power x plus 2 equals 0.

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Solve for x numerically (the equation contains functions such as sin, log or roots).

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Start with the equation.

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Rewrite as f(x) equals 0.

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This equation is not polynomial, so solve it numerically. Scan x from negative 10 to the power 9 to 10 to the power 9 for sign changes of f and for points where the graph touches the axis, then narrow each one down. Every root is checked by substituting it back.

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Found 2 solutions in [−10 to the power 9, 10 to the power 9].

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So the answer is x equals 0, x equals ln(2) approximately 0.6931471806.

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Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

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x equals 0: left side equals 0, right side equals 0, which checks out.

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x equals 0.69314718: left side equals 0, right side equals 0, which checks out.