Question

1) equação exponenciais

a) 3× =27×+³
b) (4)×+¹ = 64
c) 8× = ³√4

d) 28 ×+² 4
---- = ----
7 9

Alguém poderia me ajudar pfvr? ​

Answer 1

Resposta:

Explicação passo a passo:

$a)$

$3^{x} =27^{x+3}$

$3^{x} =(3^{3}) ^{x+3}$

$3^{x} =3^{3x+9$

$3x+9=x$

$3x-x=-9$

$2x=-9$

$x=-\frac{9}{2}$

$b)$

$4^{(x+1)} =64$

$4^{(x+1)} =4^{3}$

$x+1=3$

$x=3-1$

$x=2$

$c)$

$8^{x} =\sqrt[3]{4}$

$(2^{3}) ^{x} =4^{\frac{1}{3} }$

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

$2^{3x} =2^{\frac{2}{3} }$

$3x=\frac{2}{3}$

$x=\frac{2}{3}:3$

$x=\frac{2}{3}\:.\:\frac{1}{3}$

$x=\frac{2}{9}$

$d)$

$(\frac{27}{8}) ^{x+2} =\frac{4}{9}$

$[(\frac{3}{2}) ^{3}] ^{x+2} =(\frac{2}{3}) ^{2}$

$[(\frac{3}{2}) ^{3}] ^{x+2} =(\frac{3}{2}) ^{-2}$

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

$3x+6=-2$

$3x=-2-6$

$3x=-8$

$x=-\frac{8}{3}$