Question

resolva as equações exponenciais:

observe na foto

Answer 1

50)


a)

$2.3^{x-2}=162 \\ \\ 3^{x-2}=162/2 \\ \\ 3^{x-2}=81 \\ \\ 3^{x-2}=3^4 \\ \\ x-2=4 \\ \\ x=6$

b)

$3.5^{x-1}=75 \\ \\ 5^{x-1}=75/3 \\ \\ 5^{x-1}=25 \\ \\ 5^{x-1}=5^2 \\ \\ x-1=2 \\ \\ x=3$

c)

$5.2^{x^2-4}=160 \\ \\ 2^{x^2-4}=160/5 \\ \\ 2^{x^2-4}=32 \\ \\ 2^{x^2-4}=2^5 \\ \\ x^2-4=5 \\ \\ x^2=9 \\ \\ x= \sqrt{9} \\ \\ x=+/-3$

d)

$10.2^{x+3}=10 \\ \\ 2^{x+3}=10/10 \\ \\ 2^{x+3}=1 \\ \\ 2^{x+3}=2^0 \\ \\ x+3=0 \\ \\ x=-3$




51)


a)

$2^x+2^{x-1}=12 \\ \\ 2^x+2^x.2^{-1}=12 \\ \\ 2^x+2^x. \frac{1}{2}=12 \\ \\ 2.2^x+2^x=24 \\ \\ 3.2^x=24 \\ \\ 2^x=24/3 \\ \\ 2^x=8 \\ \\ 2^x=2^3 \\ \\ x=3$

b)

$3^{x-2}+3^{x+1}=84 \\ \\ 3^x.3^{-2}+3^x.3=84 \\ \\ 3^x. \frac{1}{3^2}+3.3^x=84 \\ \\ \frac{3^x}{9}+3.3^x=84 \\ \\ 3^x+27.3^x=756 \\ \\ 28.3^x=756 \\ \\ 3^x=756/28 \\ \\ 3^x=27 \\ \\ 3^x=3^3 \\ \\ x=3$