Substituted Indices

[Guest]

If 2n = 128, find the value of 2n-1.(5n-2)

Options: (a) 5(105) (b)2(107) (c) 2(108) (d) 2 x 105 (e) 5 x 28

[HallsofIvy]

Really? If 2n= 128 then n= 64 so (2n-1)(5n- 2)= 127(318)= 40386.

But that is not any of the given answers so I suspect that you meant 2^n= 128 so that n= 7. And your "(2n-1)(5n-2)" is probably (2^(2n-1))(5^(n-2)). With n= 7 that is (2^13)(5^5)= (8192)(3125). Hmm, that's not one of the given answers either. Perhaps now you really mean (2n-1)(5n-2)= (13)(33). No, that's not one of the given answers!

Please repost the question using "^" to indicate powers.

[HallsofIvy]

Oops. I probably should have interpreted "2n-1" as 2^(n-1), not "2^(2n-1). With n= 7, 2^(n-1)5^(n-2)= 2^6(5^5)= 64(3125)