transforme por el logaritmo de un numero desconocido ese mismo numero

a) log x= log 5-log 3+log 11 B) log y=log 6+log 3-1/5 log 5 C)log z=3 log 2-1/2 log 4+log5 D) log t=1/3log (a+b)-(log a+2 log (b+c)) E) log w=1/3(log a+1/4(log a+3 log c)

F)log x=-(log a log b-log a log b log c)

2

Respuestas

  • Usuario de Brainly
2013-11-19T22:40:35+01:00
Joven observa el procedimiento a seguir, debes utilizar las propiedades de logaritmos:

a) Log(x) = Log(5) - Log(3) + Log(11)
=> Log(x) = Log (5/3) + Log(11)
=> Log(x) = Log [ 5/3 ] [11]
=> x = (5/3)(11)
=> x = 55 / 3 ..........Respuesta.

b) Log(y) = Log(6) + Log(3) - (1/5)Log(5)

=> Log(y) = Log (6*3) - Log (5) ^(1/5)

=> Log(y)= Log [ 18 ] / [ 5^(1/5) ]

=> y = [ 18 ] / [ 5^(1/5) ] .........Respuesta:

c) Log (z) = 3 Log(2) - (1/2)Log(4) + Log(5)

=> Log(z) = Log(2)^3 - Log (4)^(1/2) + Log(5)

=> Log(z)= Log [ 8 / 4^(1/2) ] [ 5 ]

=> Log(z) = Log [ 8 / 2 ] [5]

=> Log(z) = Log [4] [5]

=> Log(z)= Log [20]

=> z = 20 ...........Respuesta.

d) Log(t) = (1/3) Log(a+b) - (Log a + (2)Log(b+c))

=> Log(t) = Log [ a+b ] ^(1/3) - (Log (a) + Log (b+c)^2)

=> Log(t)= Log [ a+b ]^3 - ( Log [a] [ (b+c)^2])

=> Log(t) = Log [ (a+b)^3 ] / [ a*(b+c)^3 ]

=> t = [ (a+b)^3 ] / [ a*(b+c)^3] ..............Respuesta.

e) Log(w) = (1/3)(Log a + (1/4)Log a + 3 Logc)

=> Log(w) = (Log a + Log a^(1/4) + 3Logc ) ^(1/3)

=> Log (w) = (Log a*a^(1/4) + Log c^3 ) ^(1/3)

=> Log(w)= ( Log a^(5/4) * c^3 ) ^(1/3)

=> w = [ a^(5/4)  * c^3 ] ^(1/3) ..........Respuesta.

Saludos.
Renedescartes
Algunos errores, pero vale el esfuerzo.
¡La mejor respuesta!
  • Usuario de Brainly
2013-11-19T23:29:20+01:00
En las preguntas donde escribi:  OJO , son las respuestas dadas incorrectamente por el usuario anterior que respondio a la pregunta.


Propiedades a utilizar:

(1) Logb A  + Logb  B  =  Logb  A.B
(2) Logb A   - Logb  B  =  Logb  A/B
(3) Logb  A = Logb B , si  y solo si :  A=B
(4) Logb  A^n = n Logb A  , y viseversa

"b" , es la base del logaritmo.
" ^ " , significa que el numero esta elevado a.
Ejm:  5^2  = 5² = 25


a) log x= log 5-log 3+log 11


   log x = log5/3 + log 11


    log x = log (5/3)(11)


    log x = log 55/3


        x = 55/3


B) log y=log 6+log 3-1/5 log 5


    log y= log(6)(3) - log5^{1/5}


    log y = log (18) - log 5{1/5}


     log y = log (18/5^{1/5} )

 y = 8/5^{1/5}

y=8/ \sqrt[5]{5}
 


C) log z=3 log 2-1/2 log 4+log5
   log z = log2³ - log4^1/2 + log5

(*) log 2³ = log 8             (*) 4^1/2 = 2

Entonces:

         log z = log 8 - log 2 + log 5
         log z = log 8/2  + log 5
         log z = log 4 + log 5
          log z = log 4.5
           log z = log 20
               z = 20

OJO:


D)log t=1/3 log (a+b)-(log a+2 log (b+c))


   log t = log (a+b)^{1/3}  -   [ log a + log (b+c)^2 ]


   log t = log (a+b)^{1/3}  -  [ log a(b+c)^2]


    log t = log (a+b)^{1/3}/                       a(b+c)²


          t =  (a+b)^{1/3} /                 a (b+c)^2




[ Opcional ] :  (a+b)^1/3 = Raiz cubica de (a+b)
                     (b+c)² = b² + 2bc + c²
 

OJO

E) log w=(1/3)(log a+1/4(log a+3 log c)

     log w = 1/3 (log a + 1/4 (log a + logc^3)


       log w = 1/3 (log a + 1/4 (log a.c^3)


       log w = 1/3 ( log a + log (a.c^3)^{1/4}


          log w = 1/3 (log a.a^{1/4} .c^{3/4} )


               log w = log [(a^{5/4})(c^{3/4})]^{1/3}


                      w = a^{5/12} .  c^{(3/4)(1/3)}


                           w = a^{5/4} . c^{1/4}

w= \sqrt[4]{a^5 . c} 




OJO:



F) log x =- (log a . log b  - log a . log b . logc]

log(x) = - ( loga^{logb} - loga^{logb.logc}

log(x) = - (log a^{logb} / a^{log b.log c} )

log (x) = - log a^{logb - logb.logc

log(x) = -1 log  a^{(logb)(1-logc)

log(x) =  log  [a^{(logb)(1-logc)]^{-1

log (x) = log a^{(logb)(logc-1)


x=a^{logb(logc-1)