Question

Sendo log 2 = 0,3 log 3 = 0,4 e log 5 = 0,7, determine:
a) log 6:
b) log 9:
c) log 2,5:
d) log 20:
e) log 30:

Answer 1

A)

$log(6) = log( 3 \times 2) = log(3) + log(2) = 0.4 + 0.3 = {\boxed{\sf \ \red{0.7}}}$

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B)

$log(9) = log(3 \times 3) = log(3) + log(3) = 0.4 + 0.4 = {\boxed{\sf \ \red{0.8}}}$

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C)

$log(2.5) \\ \\ log( \frac{25}{10} ) \\ \\ log(25) - log(10) \\ log( {5}^{2} ) - log(5 \times 2) \\ 2 \times log(5) - log(5) + log(2) \\ 2 \times 0.7 - 0.7 + 0.3 \\ 0.14 - 1 \\ {\boxed{\sf \ \red{ - 0.86}}}$

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D)

$log(20) \\ log(10 \times 2) \\ log(10) + log(2) \\ 1 + 0.3 \\ {\boxed{\sf \ \red{1.3}}}$

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E)

$log(30) \\ log(6 \times 5) \\ log(6) + log(5) \\ log(2 \times 3) + 0.7 \\ log(2) + log(3) + 0.7 \\ 0.3 + 0.4 + 0.7 \\ 0.7 + 0.7 \\ {\boxed{\sf \ \red{1.4}}}$

espero ter ajudado!