Z def. logarytmu:
[tex]log_{a}b = c \ \ to \ \ a^{c} = b[/tex]
[tex]log_{8\sqrt{2}} 4\sqrt{8} = x\\\\(8\sqrt{2})^{x} = 4\sqrt{8}\\\\(2^{3}\cdot2^{\frac{1}{2}})^{x} = 2^{2}\cdot8^{\frac{1}{2}}\\\\(2^{3+\frac{1}{2}})^{x} = 2^{2}\cdot(2^{3})^{\frac{1}{2}}\\\\(2^{\frac{7}{2}})^{x} = 2^{2}\cdot2^{3\cdot\frac{1}{2}}\\\\2^{\frac{7}{2}x}=2^{2}\cdot2^\frac{3}{2}}\\\\2^{\frac{7}{2}x}=2^{\frac{7}{2}}\\\\\frac{7}{2} x = \frac{7}{2} \ \ /\cdot\frac{2}{7}\\\\x = 1\\\\\underline{\log_{8\sqrt{2}}4\sqrt{8} = 1}[/tex]
[tex]Lub\\\\log_{8\sqrt{2}}4\sqrt{8} = log_{8\sqrt{2}}4\sqrt{4\cdot2} = log_{8\sqrt{2}}4\cdot2\sqrt{2} = log_{8\sqrt{2}}8\sqrt{2} = log_{8\sqrt{2}}(8\sqrt{2})^{1} = 1[/tex]
