Question

Evaulate 1/9^x=3^-x/3×81^x

Answer 1

Answer:

(1/9)*x = 3-(81*(x/3)*x) // - 3-(81*(x/3)*x)

81*(x/3)*x+(1/9)*x-3 = 0

27*x^2+1/9*x-3 = 0

DELTA = (1/9)^2-(-3*4*27)

DELTA = 26245/81

DELTA > 0

x = ((26245/81)^(1/2)-1/9)/(2*27) or x = (-(26245/81)^(1/2)-1/9)/(2*27)

x = ((26245/81)^(1/2)-1/9)/54 or x = (-((26245/81)^(1/2)+1/9))/54

x in { (-((26245/81)^(1/2)+1/9))/54, ((26245/81)^(1/2)-1/9)/54 }