To solve this equation, we first notice that all terms on the left side of the equation have a common factor of 2^(x-3). We can factor this out:

2^(x-3)(2^3 + 2^2 + 2^1) = 896
2^(x-3)(8 + 4 + 2) = 896
2^(x-3)(14) = 896

Now, we can divide both sides by 14 to solve for 2^(x-3):

2^(x-3) = 896 / 14
2^(x-3) = 64

Now, since 2^6 = 64, we can rewrite the equation as:

2^(x-3) = 2^6

Since the bases are the same, we can set the exponents equal to each other:

x - 3 = 6
x = 9

Therefore, the solution to the equation 2^(x-1) + 2^(x-2) + 2^(x-3) = 896 is x = 9.