Question

log 2=0,30 e log 3 0,48 o valor de log 3√12

Answer 1

Vamos lá:

Dados:

⇒$log\:2=0,3$
⇒$log\:3=0,48$
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Lembrete:

⇒$\sqrt[b]{c^a}=c^{ \frac{a}{b}$
⇒$\log _a\left(b\right)^{n\:}=n\cdot \log \:_a\left(b\right)^{n\:}$
⇒$\log _a\left(b\cdot c\right)=\log _a\:b+\log \:_a\:c$
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$log\:3\sqrt{12}\\log\:12^{\frac{1}{2}}+log\:3\\\frac{1}{2}*log\:12+log\:3\\\frac{1}{2}*log\:(3*2^2)+log\:3\\\frac{1}{2}*(log\:3+log\:2^2)\\\frac{1}{1}*(log\:3+(2*log\:2))+log\:3\\\frac{1}{2}*(0,48+2*0,3)\\\frac{1}{3}*(0,48+0,6)+0,48\\\frac{1}{2}*1,08+0,48\\0,54+0,48\\1,02$

Resposta: $log\:3\sqrt{12}=1,02$
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Espero ter ajudado!