WEBVTT

1
00:00:00.000 --> 00:00:04.609
Here is the problem: log(x minus 4, 3) equals 2.

2
00:00:05.059 --> 00:00:10.492
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.293 --> 00:00:12.721
Start with the equation.

4
00:00:13.171 --> 00:00:15.284
Rewrite as f(x) equals 0.

5
00:00:15.734 --> 00:00:31.628
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
00:00:32.078 --> 00:00:37.070
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:37.870 --> 00:00:40.436
So the answer is x equals 13.

8
00:00:40.886 --> 00:00:49.791
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:50.591 --> 00:00:56.907
x equals 13: left side equals 2, right side equals 2, which checks out.