Z definicji logarytmu
[tex]log_{a}b = c \ \ to \ \ a^{c} = b[/tex]
[tex]log_{\frac{1}{4}}\frac{1}{3} = x\\\\(\frac{1}{4})^{x} = \frac{1}{3}\\\\((\frac{1}{2})^{2})^{x} = 3^{-1}\\\\(2^{-2})^{x} = 3^{-1}\\\\2^{-2x} = 3^{-1}\\\\2^{2x} = 3\\\\log_{2}2^{2x}=log_{2} 3\\\\2x\cdot log2 = log_{2}3\\\\2x\cdot1 = log_{2}3\\\\x = \frac{1}{2}log_{2}3=log_{2}3^{\frac{1}{2}}=log_{2}\sqrt{3}\\\\\\log_{\frac{1}{4}}\frac{1}{3} = log_{2}\sqrt{3}[/tex]
