Question

60 PONTOS! POR FAVOR,AJUDA URGENTE.

Exercícios: Resolva as seguintes equações exponenciais.


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Answer 1

Resposta:

Olá!

Explicação passo-a-passo:

1. $2^x=128$

$2^x=2^7$

$x=7$

2. $3^x=243$

$3^x=3^5$

$x=5$

3. $5^x=125$

$5^x=5^3$

$x=3$

4. $4^x=64$

$4^x=4^3$

$x=3$

5. $7^x=49$

$7^x=7^2$

$x=2$

6. $2^x=512$

$2^x=2^9$

$x=9$

7. $5^x=\frac{1}{125}$

$5^x=125^{-1}$

$5^x=(5^3)^{-1}$

$x=-3$

8. $3^x=27$

$3^x=3^3$

$x=3$

9. $6^x=216$

$6^x=6^3$

$x=3$

10. $9^x=81$

$9^x=9^2$

$x=2$

1. $3^{2x}=243$

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

$2x=5=>x=\frac{5}{2}$

2. $4^x=32$

$(2^{2})^{x}=2^{5}$

$2x=5=>x=\frac{5}{2}$

3. $3^{x-1}=27$

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

$x-1=3=>x=3+1=>x=4$

4. $2^{x+3}=64$

$2^{x+3}=2^6$

$x+3=6=>x=6-3=>x=3$

5. $2^{x+1}=\frac{1}{32}$

$2^{x+1}=32^{-1}$

$2^{x+1}=(2^5)^{-1}$

$x+1=-5=>x=-5-1=>x=-6$

6. $125^x=5$

$(5^3)^{x}=5^1$

$3x=1=>x=\frac{1}{3}$

7. $3^{x+2}=81$

$3^{x+2}=3^4$

$x+2=4=>x=4-2=>x=2$

8. $5^{x+2}=125$

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

$x+2=3=>x=3-2=>x=1$

9. $4^x=\frac{1}{16}$

$4^x=(4^2)^{-1}$

$x=-2$

10. $128^x=8$

$(2^7)^{x}=2^3$

$7x=3=>x=\frac{3}{7}$

11. $125^{x+2}=1$

$(5^3)^{x+2}=5^0$

$3.(x+2)=0=>3x+6=0=>3x=-6=>x=-\frac{6}{3}=>x=-2$

12. $49^{x+2}=1$

$(7^2)^{x+2}=7^0$

$2.(x+2)=0=>2x+4=0=>2x=-4=>x=-\frac{4}{2}=>x=-2$

13. $125^x=\sqrt{5}$

$(5^3)^x=5^{\frac{1}{2} }$

$3x=\frac{1}{2}=>3x.2=1=>6x=1=>x=\frac{1}{6}$

14. $\sqrt{5^x} =25$

$5^{x.\frac{1}{2}}=5^2$

$\frac{x}{2}==>x=2.2=>x=4$

Bons Estudos!