(a^m)^n = a^(mn)
a^m*a^n = a^(m+n)
4^x - 3^(x - 1/2) = 3^(x + 1/2) - 2^(2x - 1)
4^x + 4^x/2 = 3^x(√3 + 1/√3)
4^x(1 + 1/2) = 3^x*4/√3
4^x*3/2 = 3^x*4/√3
√3 = 3^1/2
2 = 4^1/2
4^(x - 1/2)*3 = 3^(x - 1/2)*4
4^(x - 3/2) = 3^(x - 3/2)
(4/3)^(x - 3/2) = 1
x - 3/2 = 0
x = 3/2
(a^m)^n = a^(mn)
a^m*a^n = a^(m+n)
4^x - 3^(x - 1/2) = 3^(x + 1/2) - 2^(2x - 1)
4^x + 4^x/2 = 3^x(√3 + 1/√3)
4^x(1 + 1/2) = 3^x*4/√3
4^x*3/2 = 3^x*4/√3
√3 = 3^1/2
2 = 4^1/2
4^(x - 1/2)*3 = 3^(x - 1/2)*4
4^(x - 3/2) = 3^(x - 3/2)
(4/3)^(x - 3/2) = 1
x - 3/2 = 0
x = 3/2