Question

1) Resolva as equações:
a) log3 x = 4

b) log1/3 x = -2

c) log0,2 x = 6

d) log3 x+3 / x−1 = 1

Answer 1

Explicação passo-a-passo:

a)

$\sf log_{3}~x=4$

$\sf x=3^4$

$\sf x=3\cdot3\cdot3\cdot3$

$\sf \red{x=81}$

b)

$\sf log_{\frac{1}{3}}~x=-2$

$\sf x=\Big(\dfrac{1}{3}\Big)^{-2}$

$\sf x=3^2$

$\sf x=3\cdot3$

$\sf \red{x=9}$

c)

$\sf log_{0,2}~x=6$

$\sf x=(0,2)^6$

$\sf x=\Big(\dfrac{2}{10}\Big)^{6}$

$\sf x=\Big(\dfrac{1}{5}\Big)^{6}$

$\sf x=\dfrac{1}{5^6}$

$\sf x=\dfrac{1}{15625}$

$\sf \red{x=0,000064}$

d)

$\sf log_{3}~\Big(\dfrac{x+3}{x-1}\Big)=1$

$\sf \dfrac{x+3}{x-1}=3^1$

$\sf \dfrac{x+3}{x-1}=3$

$\sf x+3=3\cdot(x-1)$

$\sf x+3=3x-3$

$\sf 3x-3=x+3$

$\sf 3x-x=3+3$

$\sf 2x=6$

$\sf x=\dfrac{6}{2}$

$\sf \red{x=3}$