Solve for x 9x123x110 a xln11x0 b x1 c xlog311x1 d xlog311x0

Solve for x: 9^x123^x+11=0.

a) x=ln(11),x=0

b) x=1

c) x=log3(11),x=1

d) x=log3(11),x=0

e) x=ln(11)

f) None of the above.

9^x123^x+11=0

substitute 3^x = y ;9^x =( 3^x)^2 = y^2

So, y^2 -12y +11=0

y^2 -11y -y +11 =0

y(y-11) -1(y -11) =0

(y -1)( y -11) =0

y =1 ; 3^x =1

x =0

y = 11 ; 3^x =11

xln3 = ln11

x = ln(11)/ln3 = ln3(11)

Solution x =0 , ln3(11)

Option d