Question

log de 625 na base (5 raiz cubica de 5)

Answer 1

Vamos lá:
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Lembrete:

→ $a^n=b^k$
→ $\sqrt[c]{a^b}=a^{\frac{b}{c}}$
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$\log _{5\sqrt[3]{5}}\left(625\right)=y\\\left(_{5\sqrt[3]{5}}\right)^y=625\\\left(_{5\cdot 5^{\frac{1}{3}}}\right)^y=5^4\\\left(_{5^{1+\frac{1}{3}}}\right)^y=5^4\\\left(5^{\frac{4}{3}}\right)^y=5^4\\5^{\frac{4y}{3}}y=5^4\\------\\\frac{4y}{3}=4\\4y=3\cdot 4\\y=3$
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Resposta: $\log \:_{5\sqrt[3]{5}}\left(625\right)=3$
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Espero ter ajudado!