Wiadomo, że [latex]log_{0,25}x=-3, log_{32}y=frac{3}{5} i log_2z=6[/latex]. Oblicz iloczyn xyz.

[latex]log_{0,25}x=-3 Rightarrow x = (0,25)^{-3}= left(frac{1}{4} ight)^{-3} = 4^3 = (2^2)^3 = 2^6\ log_{32}y=frac{3}{5} Rightarrow y = 32^{frac{3}{5}} = (2^5)^{frac{3}{5}} = 2^3\ log_2z=6 Rightarrow z = 2^6\ xyz = 2^6*2^3*2^6 = 2^{6+3+6} = 2^{15} = 32768[/latex]