Question

cálculo de logaritmos decimais - calcule:

a) log 15

b) log 63

c) log 12

d) log 25
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2

Answer 1

Explicação passo-a-passo:

a)

$\sf log~15=log~(3\cdot5)$

$\sf log~15=log~3+log~5$

$\sf log~15=0,477+0,699$

$\sf \red{log~15=1,176}$

b)

$\sf log~63=log~(3^2\cdot7)$

$\sf log~63=log~3^2+log~7$

$\sf log~63=2\cdot log~3+log~7$

$\sf log~63=2\cdot0,477+0,845$

$\sf log~63=0,954+0,845$

$\sf \red{log~63=1,799}$

c)

$\sf log~12=log~(2^2\cdot3)$

$\sf log~12=log~2^2+log~3$

$\sf log~12=2\cdot log~2+log~3$

$\sf log~12=2\cdot0,301+0,477$

$\sf log~12=0,602+0,477$

$\sf \red{log~12=1,079}$

d)

$\sf log~\Big(\dfrac{25}{2}\Big)=log~25-log~2$

$\sf log~\Big(\dfrac{25}{2}\Big)=log~5^2-log~2$

$\sf log~\Big(\dfrac{25}{2}\Big)=2\cdot log~5-log~2$

$\sf log~\Big(\dfrac{25}{2}\Big)=2\cdot0,699-0,301$

$\sf log~\Big(\dfrac{25}{2}\Big)=1,398-0,301$

$\sf \red{log~\Big(\dfrac{25}{2}\Big)=1,097}$