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