WEBVTT

1
00:00:00.000 --> 00:00:04.586
Here is the problem: 4 to the power x minus 2) equals 30.

2
00:00:05.036 --> 00:00:10.678
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.478 --> 00:00:12.941
Start with the equation.

4
00:00:13.391 --> 00:00:15.469
Rewrite as f(x) equals 0.

5
00:00:15.919 --> 00:00:32.034
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
00:00:32.484 --> 00:00:37.488
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:38.288 --> 00:00:44.186
So the answer is x approximately 4.453445298.

8
00:00:44.636 --> 00:00:53.425
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:54.225 --> 00:01:03.908
x equals 4.4534453: left side equals 30, right side equals 30, which checks out.