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1. Aplicar propiedad del logaritmo a logₓ (c) = logₓ (cᵃ)
2 log (a/b) = (log(a/b)²)
2. Aplicar propiedad del logaritmo logₓ (a) - logₓ (b) = logₓ (a/b)
log (ab) - (log(a/b)²) = log ( (ab)/(a/b)² )
B. 2 ln (x-y) - ln (x²-y²)
1. Aplicar propiedad del logaritmo: a logₓ (c) = logₓ (cᵃ)
2 ln (x-y) = ln ((x-y)²)
2. Aplicar propiedad del logaritmo logₓ (a) - logₓ (b) = logₓ (a/b)
ln ((x-y)²) - ln (x²-y²) = ln ( (x-y)² / (x²-y²) )
3. Donde ( (x-y)² / (x²-y²) ) es igual a ( (x-y) / (x+y) )
Por lo tanto: ln ( (x-y)² / (x²-y²) ) = ln ( (x-y) / (x+y) )
C. ( (2 log₄ t) ( (log₄y)/3) ) + ( (z-2) (log₄ 8) )
1. Aplicar la propiedad del logaritmo: a logₓ (c) = logₓ (cᵃ)
2 log₄(t) = log₄ (t)²
( (z-2) log₄(8)) = log₄ (8∧(z-2))
(log₄y)/3) = (1/3) log₄(y) = log (∛y)
2. Tenemos:
log₄ (t)² * (log (∛y) + log₄ (8∧(z-2)) )
3. Aplicar la propiedad del logaritmo: logₓ (a) + logₓ (b) = logₓ (a*b)
(log (∛y) + log₄ (8∧(z-2)) ) = log₄ (∛y * (8∧(z-2)) )
4. Finalmente queda:
log₄ (t)² * log₄ (∛y * (8∧(z-2)))