Maths problem, how to do, i did wrong again, thanks?

2020-08-22 6:21 pm

回答 (1)

2020-08-22 6:36 pm
✔ 最佳答案
8^(a + b) = c
(2^3)^(a+b) = c
2^[3(a + b)] = c
3(a + b) = log₂(c)
               [ x = nʳ ⇔ r = logₙ(x)  as logarithm is about extracting the index ]
a + b = log₂(c) / 3
a = log₂(c) / 3 - b
a = [log₂(c) - 3b] / 3    (This is the simplest form.)

The question tricks you with one more consideration.

Consider
2 log₄(c)
= 2 log(c) / log(4)
= 2 log(c) / log(2²)
= 2 log(c) / [2 log(2)]
= log(c) / log(2)
= log₂(c)

Therefore, the answer is (A).


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