Để giải các phương trình này, chúng ta có thể sử dụng các phương pháp như chuyển đổi cơ số, sử dụng các quy tắc về lũy thừa, hoặc sử dụng các công thức đặc biệt.

1. Phương trình 5^x-1 = 10^x × 2^x × 5^x+1:
Chúng ta có thể viết lại phương trình này dưới dạng:
5^(x-1) = 10^x × 2^x × 5 × 5^x
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^x × 5
5^(x-1) = 10^x × 2^x × 5^x × 5^1
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x × 2^x × 5^(x+1)
5^(x-1) = 10^x ×