Question

considerando log de 2=0,31,log 3=0,477 e log de 5=0,699, calcule  log  150 e log  de raiz de 125

Answer 1

Propriedades Usadas:

$logaritmo~do~produto~\to~\boxed{log(b*c)~\to~logb*logc~\to~logb+logc}\\\\ logaritmo~da~potencia~\to~\boxed{logb ^{n}~\to~n*logb}$

$log150=log2*3*5 ^{2}\\ log150=log2*log3*log5 ^{2}\\ log150=log2+log3+2*log5\\ log150=0,301+0,477+0,699\\\\ \boxed{log150=1,477}$


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$log \sqrt{125}=log \sqrt[2]{5 ^{3} }\\ log \sqrt{125}=log5 ^{ \frac{3}{2} }\\\\ log \sqrt{125}= \frac{3}{2}*log5\\\\ log \sqrt{125}= \frac{3}{2}*0,699\\\\ log \sqrt{125}= \frac{0,699*3}{2}\\\\ \boxed{log \sqrt{125}=1,0485}$


Bons estudos XD