Zad. na nudę:
4.
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![b=[( \sqrt[3]{2}) ^{ \sqrt[3]{54} }]^ {^\sqrt[3]{4}](https://tex.z-dn.net/?f=b%3D%5B%28+%5Csqrt%5B3%5D%7B2%7D%29+%5E%7B+%5Csqrt%5B3%5D%7B54%7D+%7D%5D%5E+%7B%5E%5Csqrt%5B3%5D%7B4%7D+ "b=[( \sqrt[3]{2}) ^{ \sqrt[3]{54} }]^ {^\sqrt[3]{4}")
4.
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jestemt
![a = \sqrt{4^{1+log_23}} = (4^{1+log_23})^{\frac12} = 4^{\frac12+\frac12log_23} = 4^{\frac12+log_23^\frac12} = 4^\frac12*4^{log_2\sqrt3} =\\\\=2*(2^2)^{log_2\sqrt3} = 2*2^{log_23} = 2*3 = 6\\\\b=[(\sqrt[3]2)^{\sqrt[3]{54}}]^{\sqrt[3]4} = [(2^\frac13)^{\sqrt[3]{27*2}}]^{\sqrt[3]4} = 2^{\frac13*\sqrt[3]{27}*\sqrt[3]2*\sqrt[3]4} = 2^{\frac13*3*\sqrt[3]{2*4} } = \\\\=2^{\sqrt[3]8} = 2^{2} = 4\\\\a\ \textgreater \ b](https://tex.z-dn.net/?f=a+%3D+%5Csqrt%7B4%5E%7B1%2Blog_23%7D%7D+%3D+%284%5E%7B1%2Blog_23%7D%29%5E%7B%5Cfrac12%7D+%3D+4%5E%7B%5Cfrac12%2B%5Cfrac12log_23%7D+%3D+4%5E%7B%5Cfrac12%2Blog_23%5E%5Cfrac12%7D+%3D+4%5E%5Cfrac12%2A4%5E%7Blog_2%5Csqrt3%7D+%3D%5C%5C%5C%5C%3D2%2A%282%5E2%29%5E%7Blog_2%5Csqrt3%7D+%3D+2%2A2%5E%7Blog_23%7D+%3D+2%2A3+%3D+6%5C%5C%5C%5Cb%3D%5B%28%5Csqrt%5B3%5D2%29%5E%7B%5Csqrt%5B3%5D%7B54%7D%7D%5D%5E%7B%5Csqrt%5B3%5D4%7D+%3D+%5B%282%5E%5Cfrac13%29%5E%7B%5Csqrt%5B3%5D%7B27%2A2%7D%7D%5D%5E%7B%5Csqrt%5B3%5D4%7D+%3D+2%5E%7B%5Cfrac13%2A%5Csqrt%5B3%5D%7B27%7D%2A%5Csqrt%5B3%5D2%2A%5Csqrt%5B3%5D4%7D+%3D+2%5E%7B%5Cfrac13%2A3%2A%5Csqrt%5B3%5D%7B2%2A4%7D+%7D+%3D+%5C%5C%5C%5C%3D2%5E%7B%5Csqrt%5B3%5D8%7D+%3D+2%5E%7B2%7D+%3D+4%5C%5C%5C%5Ca%5C+%5Ctextgreater+%5C+b "a = \sqrt{4^{1+log_23}} = (4^{1+log_23})^{\frac12} = 4^{\frac12+\frac12log_23} = 4^{\frac12+log_23^\frac12} = 4^\frac12*4^{log_2\sqrt3} =\\\\=2*(2^2)^{log_2\sqrt3} = 2*2^{log_23} = 2*3 = 6\\\\b=[(\sqrt[3]2)^{\sqrt[3]{54}}]^{\sqrt[3]4} = [(2^\frac13)^{\sqrt[3]{27*2}}]^{\sqrt[3]4} = 2^{\frac13*\sqrt[3]{27}*\sqrt[3]2*\sqrt[3]4} = 2^{\frac13*3*\sqrt[3]{2*4} } = \\\\=2^{\sqrt[3]8} = 2^{2} = 4\\\\a\ \textgreater \ b")
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