exponential equation

[SUhottie10]

ok I think I solved this problem correctly but I'd like someone to check my work so I can make sure its right.....

1 / (16^(x-4)) = (square root of 8)^(2x^2+8)
2^[-4(x-4)] = 2^[3/2(2x^2+8)
-4(x-4) = 3/2(2x^2+8)
-4x +16 = 3x^2+12
-3x^2 - 4x+4 = 0
(-3x+2)(x+2) = 0
-3x+2 = 0 , x+2=0
x = -2/3 x=-2

Thanks!

 

[skeeter]

you know you can check your solutions by substituting what you calculated for x back into the original equation?

x = -2 works

if -3x + 2 = 0, x = 2/3, not -2/3