Question

MEEEE AJUDEEEM

Log de 0,4² na base 5/2

Log de 125 na base √x= -6

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\sf log_\frac{5}{2}\:{0,4^2}$

$\sf log_\frac{5}{2}\:{\left(\dfrac{4}{10}\right)^2}$

$\sf log_\frac{5}{2}\:{\left(\dfrac{2}{5}\right)^2}$

$\sf \left(\dfrac{5}{2}\right)^x = \left(\dfrac{2}{5}\right)^2$

$\sf \left(\dfrac{2}{5}\right)^{-x} = \left(\dfrac{2}{5}\right)^2$

$\sf -x = 2$

$\boxed{\boxed{\sf x = -2}}$

$\sf log_{\sqrt{x}}\:125 = -6$

$\sf log_{x^{\frac{1}{2}}}\:5^3 = -6$

$\sf x^{\frac{-6}{2}} = 5^3$

$\sf x^{-3} = 5^3$

$\sf x^{-3} = \left(\dfrac{1}{5}\right)^{-3}$

$\boxed{\boxed{\sf x = \dfrac{1}{5}}}$

Answer 2

Explicação passo-a-passo:

a)

$\sf log_{\frac{5}{2}}~0,4=x$

$\sf \Big(\dfrac{5}{2}\Big)^x=0,4^2$

$\sf \Big(\dfrac{5}{2}\Big)^x=\Big(\dfrac{4}{10}\Big)^2$

$\sf \Big(\dfrac{5}{2}\Big)^x=\Big(\dfrac{2}{5}\Big)^2$

$\sf \Big(\dfrac{5}{2}\Big)^x=\Big[\Big(\dfrac{5}{2}\Big)^{-1}\Big]^2$

$\sf \Big(\dfrac{5}{2}\Big)^x=\Big(\dfrac{5}{2}\Big)^{-2}$

Igualando os expoentes:

$\sf \red{x=-2}$

b)

$\sf log_{\sqrt{x}}~125=-6$

$\sf (\sqrt{x})^{-6}=125$

$\sf (x^{\frac{1}{2}})^{-6}=125$

$\sf x^{\frac{-6}{2}}=125$

$\sf x^{-3}=125$

$\sf \dfrac{1}{x^3}=125$

$\sf 125x^3=1$

$\sf x^3=\dfrac{1}{125}$

$\sf x=\sqrt[3]{\dfrac{1}{125}}$

$\sf \red{x=\dfrac{1}{5}}$