Question

va rog aceste exercitii! ​18 ,19,21 ,23 si 24

Answer 1

Răspuns:

Explicație pas cu pas:

18) lg (1/2) + lg(2/3) + ....lg(9/10) = -1 ?

lg (1/2) + lg(2/3) + ....lg(9/10) = lg(1/2 ·2/3 ·.....·9/10) =

= lg(1/10) = lg(10⁻¹) = -1lg10 = -1

19) log₃5 +log₃6 - log₃10 = log₃(5·6/10) = log₃(30/10) = log₃3 = 1

21) log₅25 - log₃9 = log₅(5²) - log₃(3²) = 2log₅5 - 2log₃3 = 2-2 = 0

23) log₆3 + log₆10 - log₆5 = log₆(3·10:5) = log₆(30:5) = log₆6 = 1

24) log₃(2/1) + log₃(3/2) +log₃(4/3) + .....+log₃(9/8) =

= log₃(2/1 ·3/2·4/3·............·9/8) = log₃9 = log₃(3²) =

= 2log₃3 = 2