[m]\sqrt[3]{2^{2x+8}}=2^{\frac{2x+8}{3}}[/m]
[m]152=2\cdot 76=2\cdot 2\cdot 38=2 \cdot 2\cdot 2\cdot 19=2^{3}\cdot 19[/m]
[m] 152\cdot 19^{2x-2}=2^{3}\cdot 19\cdot 19^{2x-2}=2^{3}\cdot 19^{2x-2+1}=2^{3}\cdot 19^{2x-1}[/m]
Уравнение:
[m]2^{\frac{2x+8}{3}}=2^{3}\cdot 19^{2x-1}[/m]
[m]2^{\frac{2x+8}{3}}\cdot 2^{-3}=19^{2x-1}[/m]
[m]2^{\frac{2x+8}{3}-3}=19^{2x-1}[/m]
[m]2^{\frac{2x-1}{3}}=19^{2x-1}[/m]
[m](2^{\frac{1}{3}})^{2x-1}=19^{2x-1}[/m]
[m]\frac{(2^{\frac{1}{3}})^{2x-1}}{19^{2x-1}}=1[/m]
[m](\frac{2^{\frac{1}{3}}}{19})^{2x-1}=1[/m]
[m]2x-1=0[/m]
[m]x=0,5[/m] - о т в е т