Question

Resuelve los ejercicios propuestos


log(15)+log(2)−log(5)


3·log(2)+2·log(3)


2·log(3)+4·log(2)−2·log(12)


log3(45)−log3(5)


log5(10)+log5(1/2)


2log(1000)+4⋅log(10)−3log(1000)



​

Answer 1

$1 \times 5 = x52yx$

Answer 2

Respuesta:

a) Log (15) + log (2) - log (5)

   $=log (5) + log (\frac{2}{5})$

   $=log (15*\frac{2}{5} )$

    $=log (6)$

b) 3·log(2) + 2·log(3)

  $=log (2^{3} ) + log (3^{2} )$

  $=log (8) + log (9)$

  $=log (8*9)$

  $=log (72)$

c)2·log(3)+4·log(2)−2·log(12)

  $=log (3^{2} ) + log (2^{4}) - log (12^{2} )$

  $=log (3^{2} ) + log (\frac{2^{4} }{12^{2} } )$

  $=log (\frac{2^{4} }{3^{2} *2^{4} } )$

  $=log (\frac{3^{2} *2^{4} }{3^{2}* 2^{4} })$

  $=log (1) \\=0$

   d) log3(45)−log3(5)

  $=log_{3} (\frac{45}{5} )$

  $=log_{3} (9)\\ \\= log_{3} (3^{2} )\\= 2$

e) log5(10)+log5(1/2)

  $=log_{5} (10*\frac{1}{2} )\\=log _{5} (5)\\=1$

f) 2log(1000)+4⋅log(10)−3log(1000)

  $=2 log (10^{3} ) + 4 log (10) - 3 log ( 10^{3} )$

  $=3*2 log (10) + 4 log (10) - 3*3 log (10)$

  $=6 log (10) + 4 log (10) - 9 log (10)\\=log (10)\\=1$

El asterisco utilizado, es para representar que se está multiplicando.