WEBVTT

1
00:00:00.000 --> 00:00:04.841
Here is the problem: 3e to the power x plus 1 equals 10.

2
00:00:05.291 --> 00:00:11.003
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.803 --> 00:00:13.277
Start with the equation.

4
00:00:13.727 --> 00:00:15.898
Rewrite as f(x) equals 0.

5
00:00:16.348 --> 00:00:32.532
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
00:00:32.982 --> 00:00:38.102
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:38.902 --> 00:00:46.228
So the answer is x equals ln(3) approximately 1.098612289.

8
00:00:46.678 --> 00:00:55.246
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:56.046 --> 00:01:05.195
x equals 1.0986123: left side equals 10, right side equals 10, which checks out.