Question

dados log2= 0,3010, log3= 0,4771, log5= 0,6990, log7= 0,8450. a) log 500; b) log 325; c) log 840; d) log 720.

Answer 1

Propriedades utilizadas:

$log\frac{a}{b}=log\,a-log\,b\\\\log(a.b)=log\,a+log\,b\\\\log\,a^c=c.log\,a$

$a)\\log500\\\\log(5.100)\\\\log(5.10^2)\\\\log5+log10^2\\\\log5+2.log10\\\\0,6990+2\;.\;1\\\\2,6990$

$b)\\log325\\\\log(5^2.13)\\\\log5^2+log13\\\\2.log5+log13\\\\2.0,6990 + 1,1139\\\\2,5119$

$log840\\\\log(2.2.2.3.5.7)\\\\log(2^3.3.5.7)\\\\3.log2+log3+log5+log7\\\\3.0,3010+0,4771+0,6990+0,8450\\\\2,9241$

$log720\\\\log(2.2.2.2.3.3.5)\\\\log(2^4.3^2.5)\\\\4.log2+2.log3+log5\\\\4.0,3010+2.0,4771+0,6990\\\\2,8572$