WEBVTT

1
00:00:00.000 --> 00:00:03.622
Here is the problem: e to the power x equals 5.

2
00:00:04.072 --> 00:00:09.738
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:10.538 --> 00:00:12.012
Start with the equation.

4
00:00:12.462 --> 00:00:14.505
Rewrite as f(x) equals 0.

5
00:00:14.955 --> 00:00:31.023
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
00:00:31.473 --> 00:00:36.430
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:37.230 --> 00:00:44.289
So the answer is x equals ln(5) approximately 1.609437912.

8
00:00:44.739 --> 00:00:53.435
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:54.235 --> 00:01:03.500
x equals 1.6094379: left side equals 5, right side equals 5, which checks out.