Question

Ajuuudem por favor !! Logaritimo


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Answer 1

Olá,

$\log_{5}(\frac{12^2}{3^2*2^4})=\log_{5}(\frac{144}{9*16})=\log_{5}(\frac{144}{144})=\log_{5}1\\\\ \log_{5}1=x\\\\ 5^x=1\\\\ \boxed{x=0}$

Answer 2

$log_{5}\left(\dfrac{12^{2}}{3^{2}\cdot2^{4}}\right)=log_{5}\left(\dfrac{12^{2}}{3^{2}\cdot(2^{2})^{2}}\right)\\\\\\log_{5}\left(\dfrac{12^{2}}{3^{2}\cdot2^{4}}\right)=log_{5}\left(\dfrac{12^{2}}{3^{2}\cdot4^{2}}\right)\\\\\\log_{5}\left(\dfrac{12^{2}}{3^{2}\cdot2^{4}}\right)=log_{5}\left(\dfrac{12^{2}}{[3\cdot4]^{2}}\right)\\\\\\log_{5}\left(\dfrac{12^{2}}{3^{2}\cdot2^{4}}\right)=log_{5}\left(\dfrac{12^{2}}{12^{2}}\right)\\\\\\log_{5}\left(\dfrac{12^{2}}{3^{2}\cdot2^{4}}\right)=log_{5}(1)$


$\boxed{\boxed{log_{5}\left(\dfrac{12^{2}}{3^{2}\cdot2^{4}}\right)=0}}$