Question

Galera listinha de 5 exercícios, 20 pontinhos ;D
segue anexo...

Answer 1

1°)
$\log_2}( x^{2} +x-4)}=3 \\ \\ x^{2} +x-4=2^3 \\ \\ x^{2} +x-4-8=0 \\ x^{2} +x-12=0$

Δ=1+48
Δ=49
√Δ=√49

$x= \frac{-b\pm \sqrt{delta} }{2a} = \frac{-1\pm7}{2} \\ \\ x'= \frac{-1+7}{2} = \frac{6}{2} =3 \\ \\ x"= \frac{-1-7}{2} =- \frac{8}{2}-4$

S={-4,3}

2°)
a)
$\log \frac{x}{3} =0 \\ \frac{x}{3} =10^0 \\ \frac{x}{3} =1 \\ x=3 \\ \\ (3,0)~~~(F)$

b)
não  (F)

c)
4-x>0
-x>-4
x<4      (V)

d)
decrescente quando 0 <a<1  (F)

e)
$f(-1)= 16^{1+ \frac{1}{-1} } \\ f(-1)= 16^{1-1} \\ f(-1)= 16^{0} \\ f(-1)=1~~~(V)$

3°)
$2^{2x+1} = \frac{1}{8} \\ \\ 2^{2x+1} =2^{-3} \\ 2x+1=-3 \\ 2x=-3-1 \\ 2x=-4 \\ x=-4\div2 \\ x=-2$

S={-2}

4°)
$V(t)=3000. 2^{0,5t} \\ V(10)=3000. 2^{0,5.10} =V(10)=3000.2^5 \\ V(10)=3000.32 \\ V(10)=96.000$

5°)
$I)~~2.3^{x-2}=162 \\ ~3^{x-2}=162\div2 \\ ~3^{x-2}=81 \\ ~3^{x-2}=3^4 \\ x-2=4 \\ x=4+2 \\ x=6$

S={6}    (V)

$II)~~3^x=10 \\ \log3^x=log10 \\ xlog3=log10 \\ x= \frac{log10}{log3} \\ \\ x= \frac{1}{0,48} ~~~(F)$

$III)~~\log_2^{(x-3)x}=2 \\ x^{2} -3x=2^2 \\ x^{2} -3x-4=0$

$(x-4)(x+1)=0 \\ \\ x-4=0 \\ x=4 \\ \\ x+1=0 \\ x=-1$

S={-1,4}    (V)

$IV)~~3^{2-x}=27^{-1} \\ ~~3^{2-x}=3^{-3} \\ 2-x=-3 \\ -x=-3-2 \\ -x=-5 \\ x=5~~~(F)$

$V)~~quando ~for~~> 1~~~~(F)$

R= 3 falsas