Answer:
x =2
Step-by-step explanation:
[tex]9^{\frac{1}{2} } \cdot 9^{\frac{1}{2} } = \sqrt[x]{81} \\\\\mathrm{Convert\:to\:base\:}9^{\frac{1}{2}}\cdot \:9^{\frac{1}{2}}:\quad 9^{\frac{1}{2}}\cdot \:9^{\frac{1}{2}}=\left(9^{\frac{1}{2}}\cdot \:9^{\frac{1}{2}}\right)^{2\cdot \frac{1}{x}}\\\\9^{\frac{1}{2}}\cdot \:9^{\frac{1}{2}}=\left(9^{\frac{1}{2}}\cdot \:9^{\frac{1}{2}}\right)^{2\cdot \frac{1}{x}}\\\\\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g(x)\\\\1=2\cdot \frac{1}{x}\\\\Simplify\\[/tex]
[tex]1=\frac{2}{x}\\\\\mathrm{Solve\:}\:1=\frac{2}{x}:\quad x=2[/tex]
