Question

Rapido! valendo 30 pontos
A)log[4] x=3
b)log1/2(2) =x
c)log 3/4(4/3) = x

Answer 1

  
  

A)log[4] x=3 ==> x = 4^3 ==> x = 64


b)log1/2(2) =x ==> 1/2^x = 2 ==> 2^-x = 2^1 ==> -x= 1(-1) ==> x = - 1


c)log 3/4(4/3) = x ==> (3/4)^x = 4/3 ==> (3/4)^x = (3/4)^-1 ==> x = - 1

Answer 2

$Resolu\c{c}\~ao(a)\to \left\{\begin{array}{ccc}log_{4}x = 3\\\\4^3 = x \\\\\boxed{x = 64}\end{array}\right$

$Resolu\c{c}\~ao(b)\to \left\{\begin{array}{ccc}log_{ \frac{1}{2} }2 =x\\\\ (\frac{1}{2})^x = 2\\\\2^{-x} = 2\\\\-x = 1 \\\\\boxed{x = -1}\end{array}\right$

$Resolu\c{c}\~ao(c)\to \left\{\begin{array}{ccc}log_{ \frac{3}{4} } \frac{4}{3} =x\\\\ (\frac{3}{4})^x = \frac{4}{3} \\\\ (\frac{4}{3})^{-x} = \frac{4}{3}\\\\-x = 1 \\\\\boxed{x = -1}\end{array}\right$

Espero ter ajudado. :))