[tex]\displaystyle\\\left(\frac{3}{4}\right)^{x+3}\cdot\frac{4}{3}=\frac{\sqrt{3}}{2}\\\\\\\left(\frac{3}{4}\right)^{x+3}=\frac{\dfrac{\sqrt{3}}{2}}{\dfrac{4}{3}}\\\\\\\left(\frac{3}{4}\right)^{x+3}=\frac{\sqrt{3}}{2}\cdot\frac{3}{4}\\\\\\\left(\frac{3}{4}\right)^{x+3}=\frac{\sqrt{3}}{\sqrt{4}}\cdot\frac{3}{4}\\\\\\\left(\frac{3}{4}\right)^{x+3}=\frac{3\sqrt{3}}{4\sqrt{4}}\\\\\\\left(\frac{3}{4}\right)^{x+3}=\frac{3^1\cdot 3^{0,5}}{4^1\cdot4^{0,5}}[/tex]
[tex]\displaystyle\\\left(\frac{3}{4}\right)^{x+3}=\frac{3^{1+0,5}}{4^{1+0,5}}\\\\\\\left(\frac{3}{4}\right)^{x+3}=\frac{3^{1,5}}{4^{1,5}}\\\\\\\left(\frac{3}{4}\right)^{x+3}=\left(\frac{3}{4}\right)^{1,5}\\\\\\x+3=1,\!5\\\\x = 1,5-3\\\\\boxed{x=-1,\!5}[/tex]
