Question

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

Answer 1

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

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

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

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

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

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

$x=1.5$