Given that x = 2log t is a solution of the equation10^(2x+1) -7(10^x) -26 =0. Find t

Answer 1

10^(2x+1) -7(10^x) -26 = 0
10*10^2x - 7*10^x - 26 = 0
10*10^(2*2log t) - 7*10^(2log t) - 26 = 0
10*10^(4log t) - 7*10^(2log t) - 26 = 0
10*(10^(log t))^4 - 7*(10^(log t))^2 - 26 = 0
10t^4 - 7t^2 - 26 = 0
(10t^2+13))(t^2-2) = 0
t = ±√2 or ±√(13/10) i