WEBVTT

1
00:00:00.000 --> 00:00:04.748
Here is the problem: log10(3x plus 2) equals 3.

2
00:00:05.199 --> 00:00:10.888
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.688 --> 00:00:13.162
Start with the equation.

4
00:00:13.612 --> 00:00:15.748
Rewrite as f(x) equals 0.

5
00:00:16.198 --> 00:00:32.127
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
00:00:32.577 --> 00:00:37.709
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:38.509 --> 00:00:42.422
So the answer is x equals 998 over 3.

8
00:00:42.872 --> 00:00:51.626
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:52.426 --> 00:01:01.819
x equals 332.66667: left side equals 3, right side equals 3, which checks out.