Question

I'm confused on how to do this.

1.) Show that f(x)=x^4 -2x +8 has nonzero constant fourth-order differences.


SIMPLIFY THE EXPRESSION: (HOW?)

2.) 8^log(8)^x
eight log root 8 ^x (here it is written if you can't understand the actual expression. It is definitely hard typing this out cuz I do not know if you could understand this/ to whomever answers.)

Answer 1

1)
x y d1 d2 d3 d4
0 8
1 7 -1
2 20 13 14
3 83 63 50 36 24
4 256 173 110 60 24
5 623 367 194 84 24
6 1292 669 302 108 24
Note how the 4th difference column is all 24 - 4th derivative of x^4 = 24

8^log_8(x) = x
exponentiation and logs are inverse operations.

b^log_b(x) = log_b(b^x) = x

the definition of log(N) is the power you need to get N, whatever the base.

and that's "to whoever answers". "whoever answers" is a noun phrase, used (as a unit) as the object of the preposition. A common mistake.