Oblicz [latex] sqrt{abc} [/latex] jeżeli : [latex] log_{a}2= frac{1}{4} [/latex] , [latex] log_{ sqrt{2} }b=8 [/latex], [latex] log_{0,25 }c=-2 [/latex] DAM NAJJ wszystkie obliczenia

[latex]1. a^{1/4} = 2, a^{1/2}=4, sqrt{a} = 4 \ 2. sqrt{2} ^8 = b, (sqrt{2} ^2)^4 = b, (2)^4 = b, b = 16, sqrt{b} = 4 \ 3. left(frac{1}{4} ight)^{-2} = c, 4^{2} = c, sqrt{c} = 4 \ Wiec sqrt{a b c} = sqrt{a} sqrt{b} sqrt{c}= 4 imes 4 imes 4 = 64[/latex]

[latex]log_a2={1over4}\ a^{1over4} = 2 / ^4\ a=2^4\ a=16\\ log_{sqrt{2}}b=8\ (sqrt{2})^8=b\ b=ig(2^{1over2}ig)^8\ b=2^4\ b=16\\ log_{0,25}c=-2\ 0,25^{-2}=c\ c=ig({1over4}ig)^{-2}\ c=4^2\ c=16\\ a=b=c\\ sqrt{abc}=sqrt{a^3}=sqrt{16^3}=sqrt{(2^4)^3}=sqrt{2^{12}}=2^6=64[/latex]