Question

Me ajudem por favor, preciso dos cálculos

1) Considerando log 2 = 0,3, log 3 = 0,4 e log 5 = 0,7, calule:

a) log2 50
b) log3 45
c) log9 2
d) log8 600
e) log5 3
f) log6 15

Answer 1

a)

$log_{2}(2 \times 25) =$

$log_{2}(2) + log_{2}(25) =$

$1 + log_{2}(5 {}^{2} ) =$

$1 + 2 log_{2}(5) = 5.64386$

b)

$log_{3}(9 \times 5) =$

$log_{3}(9) + log_{3}(5) =$

$log_{3}(3 {}^{2} ) + log_{3}(5) =$

$2 + log_{3}(5) = 3.46497$

c)

$log_{3 {}^{2} }(2) =$

$\frac{1}{2} \times log_{3}(2) = 0.315465$

d)

$log_{2 {}^{3} }(600) =$

$\frac{1}{3} \times log_{2}(600) =$

$\frac{1}{3} \times log_{2}(8 \times 75) =$

$\frac{1}{3} \times ( log_{2}(2 {}^{3} ) + log_{2}(75) ) =$

$1 + \frac{1}{3} \times log_{2}(75) = 3.07627$

e)

$\frac{ ln(3) }{ ln(5) } =$

$\frac{1.09861}{1.60944} = 0.6826$

f)

$\frac{ ln(15) }{ln(6) } =$

$\frac{2.70805}{1.79176} = 1.5114$