Question

Dados 2 = 0,301; 3 = 0,477; 5 = 0,699 7 = 0,845, calcule: a) 15 b) 14 c) 2 3 (lembre-se que uma fração corresponde a uma divisão) d) 2 4 e) 2 1 2​

Answer 1

$\boxed{\begin{array}{l}\underline{\rm D~\!\!efinic_{\!\!,}\tilde ao~de~Logaritmo}\\\sf\ell og_ba=x\Longleftrightarrow b^x=a\begin{cases}\sf a>0\\\sf b>0\\\sf b\ne1\end{cases}\\\underline{\rm propriedades~operatórias~dos~logaritmos}\\\sf\boxed{\sf1}:\ell og_c(a\cdot b)=\ell og_ca+\ell og_cb\\\sf\boxed{\sf 2}: \ell og_c\bigg(\dfrac{a}{b}\bigg)=\ell og_ca-\ell og_cb\\\sf\boxed{\sf 3}:\ell og_ca^n=n\cdot\ell og_ca\\\sf ou\\\sf \ell og_{c^n}a=\dfrac{1}{n}\ell og_ca\end{array}}$

$\boxed{\begin{array}{l}\tt a)~\sf\ell og(15)=\ell og(3\cdot5)\\\sf\ell og(15)=\ell og3+\ell og5\\\sf \ell og15=0,477+0,699=1,176\\\tt b)~\sf\ell og14=\ell og(2\cdot7)\\\sf\ell og(14)=\ell og2+\ell og7\\\sf \ell og(14)=0,301+0,845\\\sf \ell og(14)=1,146\end{array}}$

$\boxed{\begin{array}{l}\tt c)~\sf\ell og\bigg(\dfrac{2}{3}\bigg)=\ell og(2)-\ell og(3)\\\sf\ell og\bigg(\dfrac{2}{3}\bigg)=0,301-0,477\\\sf\ell og\bigg(\dfrac{2}{3}\bigg)=-0,176</p><p>\end{array}}$

$\boxed{\begin{array}{l}\tt d)~\sf\ell og2^4=4\ell og2\\\sf \ell og2^4=4\cdot0,301\\\sf \ell og2^4=1,204\end{array}}$

$\boxed{\begin{array}{l}\tt e)~\sf\ell og2^{\frac{1}{2}}=\dfrac{1}{2}\ell og2\\\sf\ell og(2^{\frac{1}{2}})=\dfrac{1}{2}\cdot0,301\\\sf \ell og(2^{\frac{1}{2}})=0,1505\end{array}}$