( 25 5 ) 5 = ( 1 5 ) x 2 − 2 {\displaystyle (25{\sqrt {5}})^{5}=({\frac {1}{5}})^{{\frac {x}{2}}-2}}
( 25 5 ) 5 = ( 1 5 ) x 2 − 2 ( 5 2 ∗ 5 1 2 ) x = 5 − ( x 2 − 2 ) 5 x = 5 − x 2 + 2 x = − x 2 + 2 2 x = − x + 4 3 x = 4 x = 4 3 {\displaystyle {\begin{aligned}(25{\sqrt {5}})^{5}=({\frac {1}{5}})^{{\frac {x}{2}}-2}\\(5^{2}*5^{\frac {1}{2}})^{x}=5^{-({\frac {x}{2}}-2)}\\5^{x}=5^{{\frac {-x}{2}}+2}\\x={\frac {-x}{2}}+2\\2x=-x+4\\3x=4\\x={\frac {4}{3}}\end{aligned}}}
