1. x^-3 +x^-3/2 = 2

assume x^-3=y

\==> y+y^1/2 =2

==> y + y^1/2 -2=0

==> (y^1/2 +2)(y^1/2 -1)=0

==> y^1/2= -2 which is impossible

==> OR y^1/2= 1 ==> y=1 ==> x= 1

2. 6(4^x + 9^x)= 6^x(9+6)

==> 6(4^x +9^x) = 6^x (13)

Divide by 6(6^x)

==> (4^x + 9^x)/6^x= 13/6

==> 4^x/6^x + 9^x/6^x = 13/6

==> (2/3)^x + (3/2)^x = 13/6

Now assume that (2/3)^x =y

==> y+ 1/y = 13/9

==> y^2 + 1 = (13/9)y

==> y^2-(13/9)y +1 =0

==> [y-(3/2)][y-(2/3)]=0

==> y = 3/2 ==> x= -1

OR y= 2/3 ==> x=1

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