WEBVTT

1
00:00:00.000 --> 00:00:04.261
Here is the problem: 27 to the power x equals 9.

2
00:00:04.711 --> 00:00:10.319
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.119 --> 00:00:12.570
Start with the equation.

4
00:00:13.020 --> 00:00:15.110
Rewrite as f(x) equals 0.

5
00:00:15.560 --> 00:00:31.570
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
00:00:32.020 --> 00:00:37.001
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:37.801 --> 00:00:40.611
So the answer is x equals 2 over 3.

8
00:00:41.061 --> 00:00:49.757
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:50.557 --> 00:01:00.193
x equals 0.66666667: left side equals 9, right side equals 9, which checks out.