(1/4)^(5x+1) = 64(4^-1)^(5x+1) = 644^(-5x-1) = 64(2^2)^(-5x-1) = 642^(-10x-2) = 642^(-10x-2) = 2^6-10x-2 = 6-10x = 8x = -8/10x = -0.8
5^x-1 + 25^x-2 = 355^x-1 + 10 5^x-2 = 355^x-1 + 10 5^x/5^2 = 355^x-1 + 10 5^(x-2) = 355^x-1 + 10 (5^x 5^-2) = 355^x-1 + 10 (5^x (1/25)) = 355^x-1 + 10/25 5^x = 355^x-1 + 2/5 5^x = 355^(x-1) + 2 5^(x-1) = 355^(x-1)(1+2) = 355^(x-1) * 3 = 355^(x-1) = 35/3x-1 = log5(35/3)x = log5(35/3) + 1
(1/4)^(5x+1) = 64
(4^-1)^(5x+1) = 64
4^(-5x-1) = 64
(2^2)^(-5x-1) = 64
2^(-10x-2) = 64
2^(-10x-2) = 2^6
-10x-2 = 6
-10x = 8
x = -8/10
x = -0.8
5^x-1 + 25^x-2 = 35
5^x-1 + 10 5^x-2 = 35
5^x-1 + 10 5^x/5^2 = 35
5^x-1 + 10 5^(x-2) = 35
5^x-1 + 10 (5^x 5^-2) = 35
5^x-1 + 10 (5^x (1/25)) = 35
5^x-1 + 10/25 5^x = 35
5^x-1 + 2/5 5^x = 35
5^(x-1) + 2 5^(x-1) = 35
5^(x-1)(1+2) = 35
5^(x-1) * 3 = 35
5^(x-1) = 35/3
x-1 = log5(35/3)
x = log5(35/3) + 1