Question

Resolva as equações exponenciais:

X+1
A) 4 =32

-x 4
B) 3 =3

2x+16 8
C) 11 =11

3x-4 8
D)3 =3

Answer 1

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a)
$4^{x+1}=32 \\ \\ (2^2)^{x+1}=2^5 \\ \\ \not2^{2x+2}=\not2^5 \\ \\ 2x+2=5 \\ \\ 2x=5-2 \\ \\ 2x=3 \\ \\ x= \frac{3}{2}$ 

b)
$\not3^{-x}=\not3^4 \\ \\ -x=4~~\times(-1) \\ \\ x=-4$ 

c)
$\not11^{2x+6}=\not11^8 \\ \\ 2x+6=8 \\ 2x=8-6 \\ 2x=2 \\ x=2\div2 \\ x=1$  

d)
$\not3^{3x-4}=\not3^8 \\ \\ 3x-4=8 \\ 3x=8+4 \\ 3x=12 \\ x=12\div3 \\ x=4$