Qual o valor do log de 625 na base 5 vezes a raiz cúbica de 5?
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Isso:![log_{(5*\sqrt[3]{5})}625](https://tex.z-dn.net/?f=log_%7B%285%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625 "log_{(5*\sqrt[3]{5})}625")
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![log_{(5*\sqrt[3]{5})}625=log_{(\sqrt[3]{5^{3}}*\sqrt[3]{5})}625\\log_{(5*\sqrt[3]{5})}625=log_{(\sqrt[3]{125}*\sqrt[3]{5})}625\\log_{(5*\sqrt[3]{5})}625=log_{(\sqrt[3]{125*5})}625\\log_{(5*\sqrt[3]{5})}625=log_{(\sqrt[3]{625})}625\\log_{(5*\sqrt[3]{5})}625=log_{(625^{\frac{1}{3}})}625\\log_{(5*\sqrt[3]{5})}625=1/(1/3)*log_{(625)}{625}\\log_{(5*\sqrt[3]{5})}625=3*1\\log_{(5*\sqrt[3]{5})}625=3](https://tex.z-dn.net/?f=log_%7B%285%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625%3Dlog_%7B%28%5Csqrt%5B3%5D%7B5%5E%7B3%7D%7D%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625%5C%5Clog_%7B%285%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625%3Dlog_%7B%28%5Csqrt%5B3%5D%7B125%7D%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625%5C%5Clog_%7B%285%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625%3Dlog_%7B%28%5Csqrt%5B3%5D%7B125%2A5%7D%29%7D625%5C%5Clog_%7B%285%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625%3Dlog_%7B%28%5Csqrt%5B3%5D%7B625%7D%29%7D625%5C%5Clog_%7B%285%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625%3Dlog_%7B%28625%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%7D625%5C%5Clog_%7B%285%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625%3D1%2F%281%2F3%29%2Alog_%7B%28625%29%7D%7B625%7D%5C%5Clog_%7B%285%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625%3D3%2A1%5C%5Clog_%7B%285%2A%5Csqrt%5B3%5D%7B5%7D%29%7D625%3D3 "log_{(5*\sqrt[3]{5})}625=log_{(\sqrt[3]{5^{3}}*\sqrt[3]{5})}625\\log_{(5*\sqrt[3]{5})}625=log_{(\sqrt[3]{125}*\sqrt[3]{5})}625\\log_{(5*\sqrt[3]{5})}625=log_{(\sqrt[3]{125*5})}625\\log_{(5*\sqrt[3]{5})}625=log_{(\sqrt[3]{625})}625\\log_{(5*\sqrt[3]{5})}625=log_{(625^{\frac{1}{3}})}625\\log_{(5*\sqrt[3]{5})}625=1/(1/3)*log_{(625)}{625}\\log_{(5*\sqrt[3]{5})}625=3*1\\log_{(5*\sqrt[3]{5})}625=3")
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