Question

$5.25^{x}-6.5^{x}+1=0$

Answer 1

    5^x = y

5y^2 - 6y + 1 = 0

delta= (-6)^2 - 4.5.1=36-20=16

y = 6 +/-V16 ==> Y = 6+/-4
           2.5                       10

y1= 6+4 ==>y1= 1
          10

y2=6-4 ==> y2 = 1
        10                 5


 5^x1 =y1 ==> 5^x1 = 1 ==> 5^x1 = 5^0 ==> x1 = 0

5^x2 =y2 ==> 5^x2 = 1/5 ==> 5^x1 = 5^-1 ==> x2 = - 1