Question

5^x+1 + 5^x + 5^x-1=31

Answer 1

$5^{x+1} + 5^x + 5^{x-1}=31 \\ {5}^{x} (5 + 1 + \frac{1}{5} ) = 31 \\ {5}^{x} \times 6 \frac{1}{5} = 31 \\ {5}^{x} \times \frac{31}{5} = 31 \\ {5}^{x} = 5 \\ x = 1$

Answer 2

$( {5}^{2} + 5 + 1) \times {5}^{x - 1} = 31 \\ \\ (25 + 5 + 1) \times {5}^{x - 1} = 31 \\ \\ 31 \times 5 {}^{x - 1} = 31 \\ \\ {5}^{x - 1} =1 {5}^{x - 1} = {5}^{0} \\ \\ x - 1 = 0 \\ \\ x = 1$