Question

Resolva as seguintes equações exponenciais; 

 

A) 16 (elevado na 2x) = 8 (elevado na x+2)
B) (0,5) (elevado na 2x) = 2(elevado na 1-3x)
C) 8 (elevado na 2-x) = (0,25) (elevado na x+1)
D) (1/3) (elevado na -x+2) = raiz de 9 elevado na 4

Answer 1

a)

$16^{2x}= 8^{x+2} \\ (2^4)^{2x}= (2^3)^{x+2} \\ 2^{8x}= 2^{3x+6}\\ 8x=3x+6\\ 8x-3x=6 \\ 5x=6 \\ x= \frac{6}{5}$

b)
$(\frac{1}{2})^x= 2^{1-3x} \\ (2^{-1})^x= 2^{1-3x}\\ 2^{-x}= 2^{1-3x} \\ -x=1-3x\\ -x+3x=1\\ 2x=1 \\ x= \frac{1}{2}$

c)

$8^{2-x}= \frac{1}{4}^{x+1}\\ (2^3)^{2-x}= (2^{-2})^{x+1} \\ 2^{6-3x}= 2^{-2x-2}\\ 6-3x=-2x-2\\ -3x+2x=-2-6\\ -x=-8 \\ x=8$

d)
$(\frac{1}{3})^{-x+2}= \sqrt[4]{9} \\ 3^{x-2}= \sqrt[4]{3^2} \\ 3^{x-2}= 3^{\frac{2}{4}} \\ 3^{x-2}= 3^\frac{1}{2}\\ x-3= \frac{1}{2} \\ x= \frac{1}{2}+3 \\ \\ x= \frac{7}{2}$