3 x ∗ 9 2 3 − x = 1 9 3 {\displaystyle 3^{\sqrt {x}}*9^{{\frac {2}{3}}-{\sqrt {x}}}={\frac {1}{\sqrt[{3}]{9}}}}
3 x ∗ 9 2 3 − x = 1 9 3 3 x ∗ 3 2 ( 2 3 − x ) = 1 9 − 1 3 3 x ∗ 3 4 3 − 2 x = 3 − 2 3 x + 4 3 − 2 x = − 2 3 4 3 − x = − 2 3 4 − 3 x = − 2 x = 2 x = 4 {\displaystyle {\begin{aligned}3^{\sqrt {x}}*9^{{\frac {2}{3}}-{\sqrt {x}}}={\frac {1}{\sqrt[{3}]{9}}}\\3^{\sqrt {x}}*3^{2({\frac {2}{3}}-{\sqrt {x}})}={\frac {1}{9^{\frac {-1}{3}}}}\\3^{\sqrt {x}}*3^{{\frac {4}{3}}-2{\sqrt {x}}}=3^{\frac {-2}{3}}\\{\sqrt {x}}+{\frac {4}{3}}-2{\sqrt {x}}={\frac {-2}{3}}\\{\frac {4}{3}}-{\sqrt {x}}={\frac {-2}{3}}\\4-3{\sqrt {x}}=-2\\{\sqrt {x}}=2\\x=4\end{aligned}}}
![{\displaystyle {\begin{aligned}3^{\sqrt {x}}*9^{{\frac {2}{3}}-{\sqrt {x}}}={\frac {1}{\sqrt[{3}]{9}}}\\3^{\sqrt {x}}*3^{2({\frac {2}{3}}-{\sqrt {x}})}={\frac {1}{9^{\frac {-1}{3}}}}\\3^{\sqrt {x}}*3^{{\frac {4}{3}}-2{\sqrt {x}}}=3^{\frac {-2}{3}}\\{\sqrt {x}}+{\frac {4}{3}}-2{\sqrt {x}}={\frac {-2}{3}}\\{\frac {4}{3}}-{\sqrt {x}}={\frac {-2}{3}}\\4-3{\sqrt {x}}=-2\\{\sqrt {x}}=2\\x=4\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b04afda29c8a01a1541903dac3403fdbfbf4c10)
![{\displaystyle 3^{\sqrt {x}}*9^{{\frac {2}{3}}-{\sqrt {x}}}={\frac {1}{\sqrt[{3}]{9}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c64f50af248739301083ac0fb59eb90a46c9e53e)