Question

me ajudem
㏒ de 5 na base √5

Answer 1

$\boxed{\begin{array}{l}\underline{\rm Logaritmo~da~pot\hat encia}\\\sf\ell og_ba^n=n\cdot\ell og_ba.\\\underline{\rm D~\!\!emonstrac_{\!\!,}\tilde ao:}\\\sf sendo~\ell og_ba=x\\\sf \ell og_ba^n=y\\\sf vamos~provar~que~ y=nx.\\\sf Com~efeito,\ell og_ba=x\implies b^x=a\\\sf\ell og_ba^n=y\implies a^n=b^y\\\sf como~a=b^x\\\sf vamos~substituir:\\\sf b^y=(b^x)^n\\\sf b^y= b^{nx}\\\sf y=nx~\boldsymbol{c\cdot q\cdot d}\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm pot\hat encia~de~expoente~racional}\\\sf\sqrt[\sf n]{\sf a^m}=a^{\frac{m}{n}}\end{array}}$

$\boxed{\begin{array}{l}\sf\ell og_5\sqrt{5}\\\sf\ell og_55^{\frac{1}{2}}\\\sf\dfrac{1}{5}\ell og_55\\\sf\dfrac{1}{5}\cdot1=\dfrac{1}{5}\end{array}}$