WEBVTT

1
00:00:00.000 --> 00:00:04.992
Here is the problem: 10 to the power 2x equals 0.01.

2
00:00:05.442 --> 00:00:11.003
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.803 --> 00:00:13.312
Start with the equation.

4
00:00:13.762 --> 00:00:15.887
Rewrite as f(x) equals 0.

5
00:00:16.337 --> 00:00:32.510
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
00:00:32.960 --> 00:00:37.918
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:38.717 --> 00:00:41.608
So the answer is x equals negative 1.

8
00:00:42.058 --> 00:00:50.754
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:51.554 --> 00:01:00.238
x equals negative 1: left side equals 0.01, right side equals 0.01, which checks out.