打圈圈的兩題，真的是不會，決對不是幫寫功課，會選最佳解，謝謝?

5)
aˣ = 6 , aʸ = 9

a²ˣ / aʸ = 4
a^((2x-y)/2) = 2

a^(y/2) = 3

24²ⁿ = 54
2^6n * 3²ⁿ = 2 * 3³
2^(6n-1) = 3^(3-2n)
a^(((2x-y)/2)(6n-1)) = a^((y/2)(3-2n))
(2x-y)(6n-1) = y(3-2n)
12xn - 6yn - 2x + y = 3y - 2yn
n(12x - 4y) = 2y + 2x
n = log_(24)_√54 = (x + y) / (6x - 2y)

..........................................................
52ᵃ = 26
2²ᵃ × 13ᵃ = 2 × 13
2²ᵃ⁻¹ = 13¹⁻ᵃ ...... (1)

52ᵇ = 5
2²ᵇ × 13ᵇ = 5 ...... (2)

104ⁿ = 130
2³ⁿ × 13ⁿ = 2 × 5 × 13
2³ⁿ⁻¹ × 13ⁿ⁻¹ = 5 ...... (3)

由(2)、(3)得
2²ᵇ × 13ᵇ = 2³ⁿ⁻¹ × 13ⁿ⁻¹
2^(2b - 3n + 1) = 13^(n - b - 1)

比較(1)知
(2b - 3n + 1) / (n - b - 1) = (2a - 1) / (1 - a)
(b - 2n) / (n - b - 1) = a / (1 - a)
b - 2n - ab + 2an = an - ab - a
a + b + an - 2n = 0
n = log_(104)_ 130 = (a + b) / (2 - a)

6)
9ᵏ = 16 , 6²ⁿ = 24
3²ᵏ = 2⁴, 2²ⁿ × 3²ⁿ = 2³ × 3
3²ᵏ = 2⁴, 3^(2n-1) = 2^(3-2n)
⇒
2k : 4 = 2n-1 : 3-2n
2(2n-1) = k(3-2n)
4n - 2 = 3k - 2kn
(2k+4)n = 3k+2
n = log_(6)_ √24 = (3k+2)/(2k+4)