Question

sabiende que el logaritmo decimal de 2 es 0,301 y que el logaritmo decimal de 3 es 0,477,calcula ayuda como se hace

Answer 1

a) log 250 = log $\frac{1000}{4}$
                 = log 1000  -  log 4
                 = log 10³ -   log 2²
                 = 3 log 10 - 2 log 2           Nota: log 10 = 1
                 = 3(1) - 2(0,301)
                 = 3 - 0,602 = 2,398

b) log 5,4  = log $\frac{54}{10}$
                 = log 54 - log 10
                 = log 2x3³ - log 10
                 = log 2 + 3 log 3 - log 10
                 = 0,301 + 3(0,477) - 1
                 = 0,301 + 1,431 - 1 = 0,732

c) log $\sqrt{18}$ = log 3$\sqrt{2}$
                                         = log 3 + 1/2 log 2
                                         = 0,477 + 1/2 (0,301)
                                         = 0,477 + 0,1505 = 0,6275

d) log 270  = log 3³.10
                  = 3 log 3 + log 10
                  = 3(0,477) + 1
                  = 1,431 + 1 = 2,431

e) log 45 = log $\frac{90}{2}$
               = log 90 - log 2
               = log 3².10 - log 2
               = 2log 3 + log 10 - log 2
               = 2(0,477) + 1 - 0,301
               = 0,954 + 1 - 0,301 = 1,653

f) log $\sqrt[3]{ \sqrt{ \frac{1}{6} } }$ = log $\sqrt[6]{ \frac{1}{6} }$
                                  = 1/6 log (1/6)
                                  = 1/6 (log 1 - log 6)
                                  = 1/6 (log 1 - log 2.3)
                                  = 1/6 (log 1 - (log 2 + log 3))
                                  = 1/6 (log 1 - log 2 - log 3)               Nota: log 1 = 0
                                  = 1/6 ( 0 - 0,301 - 0,477)
                                  = 1/6 (- 0,778) = -0,1297