Z definicji logarytmu
[tex]log_{a}b = c \ \ to \ \ a^{b} = c[/tex]
[tex]a)\\log_{2}64 = x\\\\2^{x} = 64\\\\2^{x} = 2^{6}\\\\x = 6\\\\log_{2}64 = 6[/tex]
[tex]b)\\log_{2}512 = x\\\\2^{x} = 512\\\\2^{x} = 2^{9}\\\\x = 9\\\\log_{2}512 = 9[/tex]
[tex]c)\\log_{2}0,25 = x\\\\2^{x} = 0,25\\\\2^{x} = \frac{25}{100}\\\\2^{x} = \frac{1}{4}\\\\2^{x} = (\frac{1}{2})^{2}\\\\2^{x} = 2^{-2}\\\\x = -2\\\\log_{2}0,25 = -2[/tex]
[tex]c)\\log_{2}\frac{1}{1024} = x\\\\2^{x} = \frac{1}{1024}\\\\2^{x} = (\frac{1}{2})^{10}\\\\2^{x} = 2^{-10}\\\\x = -10\\\\log_{2}1024 = -10[/tex]
