WEBVTT

1
00:00:00.000 --> 00:00:05.074
Here is the problem: 2 to the power x minus 3) equals 1 over 4.

2
00:00:05.524 --> 00:00:11.143
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.943 --> 00:00:13.406
Start with the equation.

4
00:00:13.856 --> 00:00:16.073
Rewrite as f(x) equals 0.

5
00:00:16.523 --> 00:00:32.394
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
00:00:32.844 --> 00:00:37.836
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:38.636 --> 00:00:40.737
So the answer is x equals 1.

8
00:00:41.187 --> 00:00:49.987
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:50.787 --> 00:00:59.738
x equals 1: left side equals 0.25, right side equals 0.25, which checks out.