exponential equations

Question

hi,

please help with this:

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

Answer 1

4^x - 3^{x - 1/2} = 3^{x + 1/2} - 2^{2·x - 1}

4^x - 1/3·3^{x + 1/2} = 3^{x + 1/2} - 1/2·2^{2·x}

4^x - 1/3·3^{x + 1/2} = 3^{x + 1/2} - 1/2·4^{x}

4^x + 1/2·4^{x} = 3^{x + 1/2} + 1/3·3^{x + 1/2}

3/2·4^{x} = 4/3·3^{x + 1/2}

9/8·4^{x} = 3^{x + 1/2}

9/8·4^{x} = √3·3^{x}

(4/3)^x = 8/9·√3

x = 3/2