Log de 2 sobre 3 na base 8 sobre 27
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Solução!
![log_{ \frac{8}{27} } \frac{2}{3}\\\\\\\\\
log_{ \frac{8}{27} } \frac{2}{3}=x\\\\\\
\left ( \frac{8}{27} \right )^{x}= \frac{2}{3}\\\\\\\\
\left (( \frac{2}{3})^{3} \right )^{x}= (\frac{2}{3})^{1}\\\\\\\\\
\left ( \frac{2}{3} \right )^{3x}= (\frac{2}{3})^{1}\\\\\\\\\\\
3x=1\\\\\\
\boxed{x= \frac{1}{3}}](https://tex.z-dn.net/?f=+log_%7B+%5Cfrac%7B8%7D%7B27%7D+%7D+%5Cfrac%7B2%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A+log_%7B+%5Cfrac%7B8%7D%7B27%7D+%7D+%5Cfrac%7B2%7D%7B3%7D%3Dx%5C%5C%5C%5C%5C%5C%0A+%5Cleft+%28+%5Cfrac%7B8%7D%7B27%7D+%5Cright+%29%5E%7Bx%7D%3D+%5Cfrac%7B2%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28%28+%5Cfrac%7B2%7D%7B3%7D%29%5E%7B3%7D++%5Cright+%29%5E%7Bx%7D%3D+%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B1%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C++%0A%5Cleft+%28+%5Cfrac%7B2%7D%7B3%7D+%5Cright+%29%5E%7B3x%7D%3D+%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B1%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A3x%3D1%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bx%3D+%5Cfrac%7B1%7D%7B3%7D%7D+++%0A+++ "log_{ \frac{8}{27} } \frac{2}{3}\\\\\\\\\
log_{ \frac{8}{27} } \frac{2}{3}=x\\\\\\
\left ( \frac{8}{27} \right )^{x}= \frac{2}{3}\\\\\\\\
\left (( \frac{2}{3})^{3} \right )^{x}= (\frac{2}{3})^{1}\\\\\\\\\
\left ( \frac{2}{3} \right )^{3x}= (\frac{2}{3})^{1}\\\\\\\\\\\
3x=1\\\\\\
\boxed{x= \frac{1}{3}}")
Boa tarde!
Bons estudos!
Solução!
Boa tarde!
Bons estudos!
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