WEBVTT

1
00:00:00.000 --> 00:00:04.609
Here is the problem: 4 to the power x plus 1) equals 16.

2
00:00:05.059 --> 00:00:10.643
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.443 --> 00:00:12.918
Start with the equation.

4
00:00:13.367 --> 00:00:15.468
Rewrite as f(x) equals 0.

5
00:00:15.918 --> 00:00:32.149
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
00:00:32.599 --> 00:00:37.626
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:38.426 --> 00:00:40.620
So the answer is x equals 1.

8
00:00:41.070 --> 00:00:49.998
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:50.798 --> 00:00:58.066
x equals 1: left side equals 16, right side equals 16, which checks out.