Resolva as equações:
Anexos:
Soluções para a tarefa
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Isso vai cair na minha prova amanha mdss
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Olá,
use a definição de logaritmos:
![\log_2[\log_x(x+2)]=1\\\\
\log_x(x+2)=2^1\\
\log_x(x+2)=2\\
x^2=x+2\\
x^2-x-2=0\\\\
x_1=-1\\
x_2=2\\\\
\huge\boxed{\text{S}=\{-1,2\}}](https://tex.z-dn.net/?f=%5Clog_2%5B%5Clog_x%28x%2B2%29%5D%3D1%5C%5C%5C%5C%0A%5Clog_x%28x%2B2%29%3D2%5E1%5C%5C%0A%5Clog_x%28x%2B2%29%3D2%5C%5C%0Ax%5E2%3Dx%2B2%5C%5C%0Ax%5E2-x-2%3D0%5C%5C%5C%5C%0Ax_1%3D-1%5C%5C%0Ax_2%3D2%5C%5C%5C%5C%0A%5Chuge%5Cboxed%7B%5Ctext%7BS%7D%3D%5C%7B-1%2C2%5C%7D%7D "\log_2[\log_x(x+2)]=1\\\\
\log_x(x+2)=2^1\\
\log_x(x+2)=2\\
x^2=x+2\\
x^2-x-2=0\\\\
x_1=-1\\
x_2=2\\\\
\huge\boxed{\text{S}=\{-1,2\}}")
![\log_8\{\log_3[\log_2(3x-1)]\}=0\\
\log_3[\log_2(3x-1)]=8^0\\
\log_3[\log_2(3x-1)]=1\\
\log_2(3x-1)=3^1\\
\log_2(3x-1)=3\\
3x-1=2^3\\
3x-1=8\\
3x=9\\\\
x= \dfrac{9}{3} \\\\
x=3\\\\
\huge\boxed{\text{S}=\{3\}}](https://tex.z-dn.net/?f=%5Clog_8%5C%7B%5Clog_3%5B%5Clog_2%283x-1%29%5D%5C%7D%3D0%5C%5C%0A%5Clog_3%5B%5Clog_2%283x-1%29%5D%3D8%5E0%5C%5C%0A%5Clog_3%5B%5Clog_2%283x-1%29%5D%3D1%5C%5C%0A%5Clog_2%283x-1%29%3D3%5E1%5C%5C%0A%5Clog_2%283x-1%29%3D3%5C%5C%0A3x-1%3D2%5E3%5C%5C%0A3x-1%3D8%5C%5C%0A3x%3D9%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B9%7D%7B3%7D+%5C%5C%5C%5C%0Ax%3D3%5C%5C%5C%5C%0A%5Chuge%5Cboxed%7B%5Ctext%7BS%7D%3D%5C%7B3%5C%7D%7D "\log_8\{\log_3[\log_2(3x-1)]\}=0\\
\log_3[\log_2(3x-1)]=8^0\\
\log_3[\log_2(3x-1)]=1\\
\log_2(3x-1)=3^1\\
\log_2(3x-1)=3\\
3x-1=2^3\\
3x-1=8\\
3x=9\\\\
x= \dfrac{9}{3} \\\\
x=3\\\\
\huge\boxed{\text{S}=\{3\}}")
TENHA ÓTIMOS ESTUDOS ;P
use a definição de logaritmos:
TENHA ÓTIMOS ESTUDOS ;P
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