Solve for x: `4^(x) - 3^(x-1/2)=3^(x+1/2)-2^(2x-1)`.

1.	Solve for x: `4^(x) - 3^(x-1/2)=3^(x+1/2)-2^(2x-1)`.
Answer» `4^(x)-3^(x-1/2)=3^(x+1/2) - 2 ^(2x-1)` ` or 4^(x) - 3^(x)/sqrt3 = 3^(x) sqrt3 - 4^(x)/2` ` or 3/2 xx 4^(x) = 3^(x) (sqrt3+ 1/sqrt3)` `or 3/2 xx 4^(x) = 3^(x) xx 4/sqrt3 ` `or 4^(x-1)/4^(1//2) = 3^(x-1)/sqrt3` ` or 4^(x-3//2)= 3^(x-3//2)` ` or (4/3)^(x-3//2) = 1` `or x-3/2 = 0` ` or x = 3//2`

Discussion