Question

sendo log de 2 = 0,3 e log de 3 = 0,4 determine o valor para long₂ 6? (use mudança de base)

a) 7/3 b) 8/5 c) 10/4 d) log₂ 5 e)1

ME AJUDEMM​

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm D~\!\!efinic_{\!\!,}\tilde ao~de~logaritmo}\\\sf \ell og_ba=x\Longleftrightarrow b^x=a~\begin{cases}\sf a>0\\\sf b>0\\\sf b\ne1\end{cases}\\\underline{\rm Mudanc_{\!\!,}a~de~base}\\\sf \ell og_ba=\dfrac{\ell og_ca}{\ell og_cb}\\\end{array}}$

$\Large\boxed{\begin{array}{l}\sf \ell og_26=\dfrac{\ell og6}{\ell og2}=\dfrac{\ell og(2\cdot3)}{\ell og2}\\\\\sf \ell og_26=\dfrac{\ell og2+\ell og3}{\ell og2}\\\\\sf \ell og_26=\dfrac{0,3+0,4}{0,3}\\\\\sf \ell og_26=\dfrac{0,7}{0,3}\\\\\sf \ell og_26=\dfrac{7}{3}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~a}}}}\end{array}}$