Question

Calcule o valor
A) log1000 - log3 81 - log5 5

B) log0,000001 - lo3 729 - log5 625​​

Answer 1

A) log1000 - log3 81 - log5 5

log10 10^(3) - log3 3^(4) - log5 5^(1)

(3) - (4) -(1)

-2 ✓

B) log0,000001 - lo3 729 - log5 625

log10 10^(-6) - log3 3^(6) - log5 5^(4)

(-6) -(6) -(4)

-16 ✓

Answer 2

$log(1000) - log_{3}(81) - log_{5}(5) \\ = log( {10}^{3} ) - log_{3}( {3}^{4} ) - 1 \\ = 3 log(10) - 4 log_{3}(3) - 1 \\ = (3 \times 1) - (4 \times 1) - 1 \\ = 3 - 4 - 1 = - 2$

$log(0.000001) - log_{3}(729) - log_{5}(625) \\ = log( {1 \times 10}^{ - 6} ) - log_{3}( {3}^{6} ) - log_{5}( {5}^{4} ) \\ = ( log(1) + (- 6log(10) ) - 6 log_{3}(3) - 4 log_{5}(5) \\ = (0 - 6) - (6 \times 1) - (4 \times 1) \\ = - 6 - 6 - 4 = - 16$