Find all x so that 8^(x^2)*4^x=2. Enter all the solutions, separated by commas.
+128406 8^(x^2)*4^x = 2
We can write
(2^3)^(x^2)*(2^2)^x = 2^1
[2^(3x^2) ] * [ 2^(2x) ] = 2^1
2^ [ (3x^2 + 2x) ] = 2^1 we have the bases equal....solve for the exponents
3x^2 + 2x = 1 complete the square
3(x^2 + (2/3)x + 1/9)^2 = 1 + 1/3
3 ( x + 1/3)^2 = 4/3 multiply both sides by 1/3
(x + 1/3)^2 = 4/9 take both roots
x + 1/3 = 2/3 or x + 1/3 = -2/3
x = 2/3 - 1/3 x = -2/3 - 1/3
x = 1/3 x = -1
