Question

ESCREVA NA FORMA DE UM ÚNICO LOGARITMO E RESPONDA AS SEGUINTES QUESTÕES

Answer 1

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$\boxed{\begin{array}{l}\underline{\tt Escreva~na~forma~de~um~\acute unico~logaritmo\!:}\\\tt a)~\sf\ell og_45+\ell og_49=\ell og_4(5\cdot9)=\ell og_445\\\tt b)~\sf3\ell og_84-\ell og_816=\ell og_84^3-\ell og_816\\\sf=\ell og_8\bigg(\dfrac{4^3}{16}\bigg)=\ell og_8\bigg(\dfrac{64}{16}\bigg)=\ell og_84\\\tt c)~\sf8\ell og1+\ell og0,77-\ell og0,11\\\sf=\ell og1^8+\ell og0,77-\ell og0,11\\\sf=\ell og1+\ell og0,77-\ell og0,11\\\sf=\ell og\bigg(\dfrac{1\cdot0,77}{0,11}\bigg)=\ell og7\end{array}}$

$\boxed{\begin{array}{l}\tt d)~\sf\dfrac{1}{3}\ell og_38-\ell og_310+4\ell og_32\\\sf \ell og_38^{\frac{1}{3}}-\ell og_310+\ell og_32^4\\\sf \ell og_38^{\frac{1}{3}}-\ell og_310+\ell og_32^4\\\sf=\ell og_32-\ell og_310+\ell og_316\\\sf=\ell og\bigg(\dfrac{32}{10}\bigg)=\ell og3,2\end{array}}$

$\boxed{\begin{array}{l}\underline{\tt considerando~\ell og2=0,3~,\ell og3=0,5~e~\ell og5=0,7}\\\underline{\tt determine~o~valor~de~\!:}\\\rm a)~\sf \ell og15=\ell og(3\cdot5)=\ell og3+\ell og5\\\sf=0,5+0,7=1,2\\\rm b)~\sf\ell og30=\ell og(3\cdot10)=\ell og3+\ell og10\\\sf=0,5+1=1,5\\\rm c)~\sf \ell og45=\ell og(3^2\cdot5)=2\ell og3+\ell og5\\\sf=2\cdot0,5+0,7=1+0,7=1,7\\\rm d)~\sf\ell og1,2=\ell og\bigg(\dfrac{12}{10}\bigg)=\ell og 2^2\cdot3-\ell og10\\\sf=2\ell og2+\ell og3-\ell og10\end{array}}$

$\boxed{\begin{array}{l}\sf \el log1,2=2\cdot0,3+0,5-1=1,1-1=0,1\\\rm e)~\sf\ell og(1,5)^2=\ell og\bigg(\dfrac{3}{2}\bigg)^2=[\ell og3-\ell og2]^2\\\sf=[0,5-0,3]^2=0,2^2=0,04\end{array}}$

$\boxed{\begin{array}{l}\tt f)~\sf\ell og\sqrt{0,3}\\\sf=\ell og\bigg(\dfrac{3}{10}\bigg)^{\frac{1}{2}}\\\sf=\dfrac{1}{2}\cdot[\ell og3-\ell og10]\\\sf=\dfrac{1}{2}[0,5-1]=\dfrac{1}{2}\cdot[-0,5]=0,5\cdot[-0,5]=-0,25\end{array}}$