WEBVTT

1
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Here is the problem: 5 to the power 2x equals 125.

2
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Solve for x numerically (the equation contains functions such as sin, log or roots).

3
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Start with the equation.

4
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Rewrite as f(x) equals 0.

5
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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.

6
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Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
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So the answer is x equals 3 over 2.

8
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Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
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x equals 1.5: left side equals 125, right side equals 125, which checks out.