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👨🏻‍🏫 學術台數學

Mcc

2020-09-10 10:36 pm

Show that 2^(x+1) + 6(2^(x-1)) = 12 can be written as 2(2^(x)) + 3(2^(x)) = 12
I don't get it :(((

回答 (2)

用戶26240

2020-09-10 11:41 pm

✔ 最佳答案

Law of indices:
nᵃ⁺ᵇ = nᵃ*nᵇ
nᵃ⁻ᵇ = nᵃ/nᵇ

2ˣ⁺¹ + 6(2ˣ⁻¹) = 12
2ˣ * 2¹ + 6(2ˣ/2¹) = 12
2(2ˣ) + 3(2ˣ / 2) = 12

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用戶58503

2020-09-10 10:41 pm

2^(x+1) = 2^x * 2^1 = 2^x * 2 = 2 * 2^x.

Apply the same reasonings to 6(2^(x-1)).

All good?

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