Question

1- Sabendo-se que log=27 ,log=−1/27 log = 3, pede-se:

log3.2

Answer 1

propriedades de log :

$\displaystyle \sf \log_{c}(a\cdot b) = \log_{c}a+\log_{c}b\\\\ \log_{c}\left(\frac{a}{b}\right) = \log_{c} a-\log_{c} b\\\\ \log_{c} a^b = b\cdot \log_{c}a$

Temos :

$\displaystyle\sf \log_{a}x=n \ ,\ \log_{a}y=\frac{-1}{n} \ , \ \log_{a}z = 3 \\\\\\ \log_{a}\left(\frac{x^3\cdot z}{y^2}\right) \\\\\\\ \log_{a}\left(x^3\cdot z\right)-\log_{a}y^2 \\\\ \log_{a}x^3+\log_{a}z-\log_{a}y^2 \\\\ 3\log_{a} x+\log_{a}z-2\log_{a} y \\\\ 3\cdot n+3-2\cdot \left(\frac{-1}{n}\right) \\\\\\ 3n+3+\frac{2}{n}$

$\displaystyle \sf Portanto : \\\\ \boxed{\sf \log_{a}\left(\frac{x^3\cdot z}{y^2}\right)=3n+\frac{2}{n}+3 \ }\checkmark \\\\\\ OU \\ (tirando \ o \ MMC ) : \\\\ \boxed{\sf \log_{a}\left(\frac{x^3\cdot z}{y^2}\right)=\frac{3n^2+3n+2}{n} \ }\checkmark$