f(x) | = | a * xr | ||
f(2) | = | a * 2r | ||
Since f(2) = 1 , we can replace f(2) with 1 . | ||||
1 | = | a * 2r | ||
Divide both sides of the equation by 2r . | ||||
12r | = | a |
f(32) | = | a * 32r | ||
Since f(32) = 4 , we can replace f(32) with 4 . | ||||
4 | = | a * 32r | ||
Divide both sides of the equation by 32r . | ||||
432r | = | a |
And since a = a .....
12r | = | 432r | ||
Since 20 = 1 , 22 = 4 , and 25 = 32 , we can say... | ||||
202r | = | 22(25)r | ||
And (xa)b = xab | ||||
202r | = | 2225r | ||
And xaxb=xa−b | ||||
20 - r | = | 22 - 5r | ||
Now the bases are equal, so the exponents are equal. | ||||
0 - r | = | 2 - 5r | ||
0 | = | 2 - 4r | ||
-2 | = | -4r | ||
12 | = | r |