Задача 56873 sqrt^3((4^x)*sqrt8))...

5f54df62356816184059ff63

12.01.2021 11:52:27

sqrt^3((4^x)*sqrt8)) =0,125*sqrt^4((2^(x+1)*sqrt^3(0,25^x))

5f3ea7e3faf909182968ddd9

12.01.2021 14:48:04

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[m]\sqrt[3]{4^{x}\cdot \sqrt{8}}=0,125\cdot \sqrt[4]{2^{x+1}\cdot \sqrt[3]{0,25^{x}}}[/m]


[m](2^{2x}\cdot 2^{\frac{3}{2}}))^{\frac{1}{3}}=2^{-8}\cdot (2^{x+1}\cdot((2^{-2})^{x})^{\frac{1}{3}})^{\frac{1}{4}}[/m]

[m](2^{\frac{4x+3}{2}})^{\frac{1}{3}}=2^{-8}\cdot (2^{x+1-\frac{2x}{3}})^{\frac{1}{4}}[/m]

[m]2^{\frac{4x+3}{6}}=2^{-8+\frac{x+3}{3}\cdot \frac{1}{4}}[/m]

[m]\frac{4x+3}{6}=-8+\frac{x+3}{12}[/m]

[m]\frac{4x+3}{6}=\frac{-96+x+3}{12}[/m]

[m]\frac{4x+3}{6}=\frac{x-93}{12}[/m]

[m]4x+3=\frac{x-93}{2}[/m]

[m]8x+6=x-93[/m]

[m]7x=-99[/m]

[m]x=-\frac{99}{7}[/m]