Question

calcule o logarítimo: log1/7 7 7√7 preciso da resposta o mais rapido possivel, obrigado.

Answer 1

Explicação passo-a-passo:

Veja que:

$7\sqrt[7]{7}=7^1\cdot7^{\frac{1}{7}}=7^{1+\frac{1}{7}}=7^{\frac{8}{7}}$

$\dfrac{1}{7}=7^{-1}$

Lembre-se que:

$\text{log}_{b^{\beta}}~a^{\alpha}=\dfrac{\alpha}{\beta}\cdot\text{log}_{b}~a$

Assim:

$\text{log}_{\frac{1}{7}}~7\sqrt[7]{7}=\text{log}_{7^{-1}}~7^{\frac{8}{7}}$

$\text{log}_{\frac{1}{7}}~7\sqrt[7]{7}=\dfrac{\frac{8}{7}}{-1}\cdot\text{log}_{7}~7$

$\text{log}_{\frac{1}{7}}~7\sqrt[7]{7}=\dfrac{-8}{7}\cdot1$

$\text{log}_{\frac{1}{7}}~7\sqrt[7]{7}=\dfrac{-8}{7}$