Question

Se x > 0 e x != 1 e log(x)7 = - 1/3, calcule log(1/x)7^6​

Answer 1

Explicação passo-a-passo:

Lembre-se que:

• $\sf log_{b^m}~a~=\dfrac{1}{m}\cdot log_{b}~a$

• $\sf log_{b}~a^n=n\cdot log_{b}~a$

Assim:

$\sf E=log_{\frac{1}{x}}7^6$

$\sf E=log_{x^{-1}}~7^6$

$\sf E=\dfrac{1}{-1}\cdot log_{x}~7^6$

$\sf E=(-1)\cdot log_{x}~7^6$

$\sf E=6\cdot(-1)\cdot log_{x}~7$

$\sf E=6\cdot(-1)\cdot\Big(-\dfrac{1}{3}\Big)$

$\sf E=\dfrac{6}{3}$

$\sf \red{E=2}$