We know that 7 ^ a = 5,49 ^ A + B = 81,7 ^ C = 35,7 ^ D = 63, and prove that B + C = D

We know that 7 ^ a = 5,49 ^ A + B = 81,7 ^ C = 35,7 ^ D = 63, and prove that B + C = D

7^a=5
7^2a=5²=25
49^(a+b)=81
7^2(a+b)=81
7^2a•7^2b=81
25•7^2b=81
5²•7^2b=81
(5•7^b)²=81
5•7^b=9
7^b=9/5 (1)
7^c=35,(2)
(1) By (2)
7^b•7^c=7^(b+c)
7^b•7^c=(9/5)•35=9•7=63
7^(b+c)=63
And: 7 ^ D = 63
So: 7 ^ (B + C) = 7 ^ D
That is to say: B + C = D

Let the coefficient of x ^ 3 in the constant a > 0, (AX-1 / x) ^ 5 expansion be - (5 / 81), then a = I, the answer is 1 / 3, but the answer is 1 / 2

Using Yang Hui's triangle or formula to expand, the term x ^ 3 is - 5A ^ 4x ^ 3, and its coefficient is - 5A ^ 4 = - 5 / 81 〈 a ^ 4 = 1 / 81, which can be obtained from a > 0, a = 1 / 3. The answer should be wrong

In the expansion of (a + 1) ^ n, the binomial coefficient of the third term is 21, and the sixth term is 63, then a is

The second term of the third term is the coefficient C2, n = n * (n - 1) / 2 = 21, so n = 7
Item 6 is (C 67) * a ^ 2 = (C 17) * a ^ 2 = 7a ^ 2 = 63, so a = 3