Logaritmo ajudem por favorr ![Log \frac{1}{27} \sqrt[4]{729}](https://tex.z-dn.net/?f=Log+%5Cfrac%7B1%7D%7B27%7D+++%5Csqrt%5B4%5D%7B729%7D+ "Log \frac{1}{27} \sqrt[4]{729}")
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Sem aplicar a definição de logaritmos:
![log_{(\frac{1}{27})}(\sqrt[4]{729})=log_{(\frac{1}{3^{3}})}(\sqrt[4]{3^{6}})\\log_{(\frac{1}{27})}(\sqrt[4]{729})=log_{(3^{-3})}(\sqrt[2]{3^{3}})](https://tex.z-dn.net/?f=log_%7B%28%5Cfrac%7B1%7D%7B27%7D%29%7D%28%5Csqrt%5B4%5D%7B729%7D%29%3Dlog_%7B%28%5Cfrac%7B1%7D%7B3%5E%7B3%7D%7D%29%7D%28%5Csqrt%5B4%5D%7B3%5E%7B6%7D%7D%29%5C%5Clog_%7B%28%5Cfrac%7B1%7D%7B27%7D%29%7D%28%5Csqrt%5B4%5D%7B729%7D%29%3Dlog_%7B%283%5E%7B-3%7D%29%7D%28%5Csqrt%5B2%5D%7B3%5E%7B3%7D%7D%29 "log_{(\frac{1}{27})}(\sqrt[4]{729})=log_{(\frac{1}{3^{3}})}(\sqrt[4]{3^{6}})\\log_{(\frac{1}{27})}(\sqrt[4]{729})=log_{(3^{-3})}(\sqrt[2]{3^{3}})")
Sabemos que![\sqrt[b]{x^{a}}=x^{\frac{a}{b}}](https://tex.z-dn.net/?f=%5Csqrt%5Bb%5D%7Bx%5E%7Ba%7D%7D%3Dx%5E%7B%5Cfrac%7Ba%7D%7Bb%7D%7D "\sqrt[b]{x^{a}}=x^{\frac{a}{b}}")
e 
![log_{(\frac{1}{27})}(\sqrt[4]{729})=\frac{1}{-3}\cdot log_{3}(3^{\frac{3}{2}})\\log_{(\frac{1}{27})}(\sqrt[4]{729})=-\frac{1}{3}\cdot\frac{3}{2}\cdot log_{3}(3)\\log_{(\frac{1}{27})}(\sqrt[4]{729})=-\frac{1}{2}\cdot1\\\\\\\boxed{\boxed{log_{(\frac{1}{27})}(\sqrt[4]{729})=-\dfrac{1}{2}}}](https://tex.z-dn.net/?f=log_%7B%28%5Cfrac%7B1%7D%7B27%7D%29%7D%28%5Csqrt%5B4%5D%7B729%7D%29%3D%5Cfrac%7B1%7D%7B-3%7D%5Ccdot+log_%7B3%7D%283%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5C%5Clog_%7B%28%5Cfrac%7B1%7D%7B27%7D%29%7D%28%5Csqrt%5B4%5D%7B729%7D%29%3D-%5Cfrac%7B1%7D%7B3%7D%5Ccdot%5Cfrac%7B3%7D%7B2%7D%5Ccdot+log_%7B3%7D%283%29%5C%5Clog_%7B%28%5Cfrac%7B1%7D%7B27%7D%29%7D%28%5Csqrt%5B4%5D%7B729%7D%29%3D-%5Cfrac%7B1%7D%7B2%7D%5Ccdot1%5C%5C%5C%5C%5C%5C%5Cboxed%7B%5Cboxed%7Blog_%7B%28%5Cfrac%7B1%7D%7B27%7D%29%7D%28%5Csqrt%5B4%5D%7B729%7D%29%3D-%5Cdfrac%7B1%7D%7B2%7D%7D%7D "log_{(\frac{1}{27})}(\sqrt[4]{729})=\frac{1}{-3}\cdot log_{3}(3^{\frac{3}{2}})\\log_{(\frac{1}{27})}(\sqrt[4]{729})=-\frac{1}{3}\cdot\frac{3}{2}\cdot log_{3}(3)\\log_{(\frac{1}{27})}(\sqrt[4]{729})=-\frac{1}{2}\cdot1\\\\\\\boxed{\boxed{log_{(\frac{1}{27})}(\sqrt[4]{729})=-\dfrac{1}{2}}}")
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Aplicando a definição de logaritmos:
![log_{(\frac{1}{27})}(\sqrt[4]{729})=x\\\\(\frac{1}{27})^{x}=\sqrt[4]{729}\\\\(3^{-3})^{x}=\sqrt[4]{3^{6}}\\\\3^{-3x}=3^{\frac{6}{4}}\\\\\\-3x=\frac{6}{4}\\\\-x=\frac{2}{4}\\\\-x=\frac{1}{2}\\\\\\\boxed{\boxed{x=-\dfrac{1}{2}}}](https://tex.z-dn.net/?f=log_%7B%28%5Cfrac%7B1%7D%7B27%7D%29%7D%28%5Csqrt%5B4%5D%7B729%7D%29%3Dx%5C%5C%5C%5C%28%5Cfrac%7B1%7D%7B27%7D%29%5E%7Bx%7D%3D%5Csqrt%5B4%5D%7B729%7D%5C%5C%5C%5C%283%5E%7B-3%7D%29%5E%7Bx%7D%3D%5Csqrt%5B4%5D%7B3%5E%7B6%7D%7D%5C%5C%5C%5C3%5E%7B-3x%7D%3D3%5E%7B%5Cfrac%7B6%7D%7B4%7D%7D%5C%5C%5C%5C%5C%5C-3x%3D%5Cfrac%7B6%7D%7B4%7D%5C%5C%5C%5C-x%3D%5Cfrac%7B2%7D%7B4%7D%5C%5C%5C%5C-x%3D%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5C%5C%5Cboxed%7B%5Cboxed%7Bx%3D-%5Cdfrac%7B1%7D%7B2%7D%7D%7D "log_{(\frac{1}{27})}(\sqrt[4]{729})=x\\\\(\frac{1}{27})^{x}=\sqrt[4]{729}\\\\(3^{-3})^{x}=\sqrt[4]{3^{6}}\\\\3^{-3x}=3^{\frac{6}{4}}\\\\\\-3x=\frac{6}{4}\\\\-x=\frac{2}{4}\\\\-x=\frac{1}{2}\\\\\\\boxed{\boxed{x=-\dfrac{1}{2}}}")
Sabemos que
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Aplicando a definição de logaritmos:
Usuário anônimo:
niyya resolve mais uma peergunta minha eu vou te mandar o link ninguem resolve
http://brainly.com.br/tarefa/1372392
pronto :)
valeu voce é demais (: prova amanha de recuperação entao ja viu ne hauaha
niiya sem querer ser chato voce pode resolver so mais uma tarefa pra mim , eu vou fazer a pergunta e mando aqui
http://brainly.com.br/tarefa/1372496
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