A solução da equação 9 ^-x +23 = 1/81 é o número Q. O valor do logaritmo de Q na base 5 é igual a:
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em anexo segue a questão!
Anexos:
Soluções para a tarefa
Respondido por
25
Boa noite João!
Solução!
Primeiro vamos resolver a equação exponencial!
![9^{-x+23}= \frac{1}{81}\\\\\\
Lembrando!\\\\\\\
9=3^{2}\\\\\
81=3^{4}\\\\\\
3^{2} ^{(-x+23)}= \frac{1}{3^{4} }\\\\\\\\\
3^{2} ^{(-x+23)}= 3^{-4} \\\\\\\\\
3 ^{(-2x+46)}= 3^{-4} \\\\\\\\\
Veja~~que~~as~~bases~~est\~ao~~iguais](https://tex.z-dn.net/?f=9%5E%7B-x%2B23%7D%3D+%5Cfrac%7B1%7D%7B81%7D%5C%5C%5C%5C%5C%5C%0ALembrando%21%5C%5C%5C%5C%5C%5C%5C%0A9%3D3%5E%7B2%7D%5C%5C%5C%5C%5C%0A81%3D3%5E%7B4%7D%5C%5C%5C%5C%5C%5C%0A3%5E%7B2%7D+%5E%7B%28-x%2B23%29%7D%3D+%5Cfrac%7B1%7D%7B3%5E%7B4%7D+%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A3%5E%7B2%7D+%5E%7B%28-x%2B23%29%7D%3D+3%5E%7B-4%7D+%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A3+%5E%7B%28-2x%2B46%29%7D%3D+3%5E%7B-4%7D+%5C%5C%5C%5C%5C%5C%5C%5C%5C%0AVeja%7E%7Eque%7E%7Eas%7E%7Ebases%7E%7Eest%5C%7Eao%7E%7Eiguais "9^{-x+23}= \frac{1}{81}\\\\\\
Lembrando!\\\\\\\
9=3^{2}\\\\\
81=3^{4}\\\\\\
3^{2} ^{(-x+23)}= \frac{1}{3^{4} }\\\\\\\\\
3^{2} ^{(-x+23)}= 3^{-4} \\\\\\\\\
3 ^{(-2x+46)}= 3^{-4} \\\\\\\\\
Veja~~que~~as~~bases~~est\~ao~~iguais")
![-2x+46=-4\\\\\
-2x=-4-46\\\\\
-2x=-50\\\\\
x= \dfrac{-50}{-2}\\\\\\
\boxed{x=25}\\\\
logo!\\\\\
x=Q=25](https://tex.z-dn.net/?f=-2x%2B46%3D-4%5C%5C%5C%5C%5C%0A-2x%3D-4-46%5C%5C%5C%5C%5C%0A-2x%3D-50%5C%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B-50%7D%7B-2%7D%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bx%3D25%7D%5C%5C%5C%5C%0Alogo%21%5C%5C%5C%5C%5C%0Ax%3DQ%3D25+ "-2x+46=-4\\\\\
-2x=-4-46\\\\\
-2x=-50\\\\\
x= \dfrac{-50}{-2}\\\\\\
\boxed{x=25}\\\\
logo!\\\\\
x=Q=25")
![Fazendo!\\\\\
logQ_{5}\\\\\\
log_{5}25\\\\\\
log_{5}25=y\\\\\\
25=5^{y} \\\\\\
5^{2}=5^{y} \\\\\\\
\boxed{y=2} \\\\\\\\
\boxed{Resposta:~~y=2~~~~\boxed{Alternativa~~D}}](https://tex.z-dn.net/?f=Fazendo%21%5C%5C%5C%5C%5C%0AlogQ_%7B5%7D%5C%5C%5C%5C%5C%5C+%0Alog_%7B5%7D25%5C%5C%5C%5C%5C%5C%0Alog_%7B5%7D25%3Dy%5C%5C%5C%5C%5C%5C%0A25%3D5%5E%7By%7D+%5C%5C%5C%5C%5C%5C%0A5%5E%7B2%7D%3D5%5E%7By%7D+%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7By%3D2%7D+%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3A%7E%7Ey%3D2%7E%7E%7E%7E%5Cboxed%7BAlternativa%7E%7ED%7D%7D "Fazendo!\\\\\
logQ_{5}\\\\\\
log_{5}25\\\\\\
log_{5}25=y\\\\\\
25=5^{y} \\\\\\
5^{2}=5^{y} \\\\\\\
\boxed{y=2} \\\\\\\\
\boxed{Resposta:~~y=2~~~~\boxed{Alternativa~~D}}")
Boa noite!
Bons estudos!
Solução!
Primeiro vamos resolver a equação exponencial!
Boa noite!
Bons estudos!
joaoxt:
Obrigado meu amigo ! tem mais uma lá se puder me ajudar te agradeço !
Respondido por
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Resposta:
Explicação passo-a-passo:
o meu esta aparecendo d outra forma vcs podem mim ajudar ?
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