Lembre-se:
[tex]1/x^{n} = x^{-n}[/tex]
[tex] \sqrt[n]{x^{y}} = x^{y/n}[/tex]
[tex]log_{(x^{n})}(a) = (1 / n) * log_{x} (a)[/tex]
[tex]log_{(x)} (x) = 1[/tex]
[tex]log_{(x)}(a) = n <=> x^{n} = a[/tex]
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[tex]log_{(1/4)} (2\sqrt{2}) =log_{(1/2^{2})} (2 \sqrt{2})[/tex]
[tex]log_{(1/4)}(2 \sqrt{2})= log_{(2^{-2})}(2*2^{1/2})[/tex]
[tex]log_{(1/4)}(2 \sqrt{2})= (1 / [-2]) * log_{(2)} (2^{1}*2^{1/2})[/tex]
[tex]log_{(1/4)}(2 \sqrt{2})= - (1 / 2) * log_{(2)} (2^{1+1/2})[/tex]
[tex]log_{(1/4)}(2 \sqrt{2})= - (1 / 2) * log_{(2)} (2^{3/2})[/tex]
[tex]log_{(1/4)}(2 \sqrt{2})= - (1 / 2) * (3 / 2) * log_{(2)} 2[/tex]
[tex]log_{(1/4)}(2 \sqrt{2})=- (3 / 4) * 1[/tex]
[tex]log_{(1/4)}(2 \sqrt{2})=-3/4[/tex]
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Outro método:
[tex]log_{(1/4)} (2 \sqrt{2} ) = x[/tex]
[tex](1/4)^{x} = 2 \sqrt{2} [/tex]
[tex](1/2^{2})^{x} = \sqrt{2*2^{2}} [/tex]
[tex](2^{-2})^{x} = \sqrt{2^{3}} [/tex]
[tex]2^{-2x} = 2^{3/2}[/tex]
Bases iguais, iguale os expoentes:
[tex]-2x=3/2[/tex]
[tex]2x=-3/2[/tex]
[tex]2*2x=-3[/tex]
[tex]4x=-3[/tex]
[tex]x=-3/4[/tex]
