Question

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)

Answer 1

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:

$F) log x =- (log a . log b - log a . log b . logc] log(x) = - ( loga^{logb} - loga^{logb.logc} log(x) = - (log a^{logb} / a^{log b.log c} ) log (x) = - log a^{logb - logb.logc log(x) = -1 log a^{(logb)(1-logc) log(x) = log [a^{(logb)(1-logc)]^{-1 log (x) = log a^{(logb)(logc-1) x=a^{logb(logc-1)$