Question

$4^{x}-3^{x-frac{1}{2}}=3^{x+frac{1}{2}}-2^{2x-1}$

Answer 1

$4^x+0.5times 4^x = frac{3^x}{sqrt{3}}+sqrt{3}times 3^x$

$frac{3}{2}times 4^x = frac{3^x+3times 3^x}{sqrt{3}}$

$frac{3times 4^x}{2}= frac{4times 3^x}{sqrt{3}}$

$3times 4^xtimes sqrt{3}=4times 3^x times 2$

$(frac{3}{4})^x=frac{3times sqrt{3}}{8}$

$(frac{3}{4})^x=(frac{3}{4})^{frac{3}{2}}$

$x=1.5$