Question

"Resolva as equações exponenciais, utilizando fatoração" pfv galera me ajuda, valendo 100 pontos​

Answer 1

Explicação passo-a-passo:

K)

$3 {}^{2x} = 243$

$3 {}^{2x} = 3 {}^{5}$

$2x = 5$

x=>5/2

L)

$27 {}^{x} = 81$

$3 {}^{3x} = 3 {}^{4}$

$3x = 4$

x=>4/3

M)

$8 {}^{x} = \dfrac{1}{4}$

$2 {}^{3x} = - 2$

$3x = - 2$

x=>-2/3

N)

$7 {}^{3x + 4} = 49 {}^{2x - 3}$

$7 {}^{3x + 4} = 7 {}^{4x - 6}$

$3x + 4 = 4x - 6$

$3x - 4x = - 6 - 4$

$- x = - 10( - 1)$

x=>10

O)

$5 {}^{x} = \dfrac{1}{125}$

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

x=>-3

P)

$729 {}^{2x} = 27$

$27 {}^{4x} = 27 {}^{1}$

$4x = 1$

x=>1/4

Q)

$3 {}^{x - 1} = 81$

$3 {}^{x - 1} = 3 {}^{4}$

$x - 1 = 4$

$x = 4 + 1$

x=>5

R)

$( \dfrac{1}{3} ) {}^{x} = 81$

$3 {}^{ - x} = 3 {}^{4}$

$- x = 4( - 1)$

x=>-4

S)

$2 {}^{x - 2} = 8$

$2 {}^{x - 2} = 2 {}^{3}$

$x - 2 = 3$

$x = 3 + 2$

x=>5

T)

$4 {}^{x} = 512$

$2 {}^{2x} = 2 {}^{9}$

$2x = 9$

x=>9/2