Question

Sabendo que log 2 = 0,301; log 3= 0,477 e log 5 =0,699. Calcule o valor das expressões aplicando as propriedades dos logaritmos:
a) log 100 + log 50 + log 10 + log 2
b) 2 log 8 + log 45-5 log 9.

COM CALCULOS!

Answer 1

a) $\log100+\log50+\log10+\log2=$

$\log(2^2\cdot 5^2)+\log(2\cdot5^2)+\log(2\cdot5)+\log2=$

$\log2^2+\log5^2+\log2+\log5^2+\log2+\log5+\log2=$

$2\log2+2\log5+\log2+2\log5+\log2+\log5+\log2=$

$5\log2+5\log5=$

$5(\log2+\log5)=$

$5(0,301+0,699)=$

$5\cdot1=$

$5$

b) $2\log8+\log45-5\log9=$

$2\log2^3+\log(3^2\cdot 5)-5\log3^2=$

$2\cdot3\log2+\log3^2+\log5-5\cdot 2\log3=$

$6\log2+2\log3+\log5-10\log3=$

$6\log2-8\log3+\log5=$

$6\cdot 0,301-8\cdot 0,477+0,699=$

$1,806-3,816+0,699=$

$-1,311$