Question

Determinați logaritmii următoarelor numere​

Answer 1

Răspuns:

Explicație pas cu pas:

1) 27 ; 1 ; 1/9 ; 1/∛3  ; ∛9 ; 9/⁴√3 ; 3^√3  in baza 3

log₃ 27 = log₃(3³) = 3·log₃3 = 3

log₃1 = log₃(3⁰) = 0

log₃(1/9) = log₃(3⁻²) = -2

log₃( 1/∛3) = log₃(3⁻¹⁽³) = -1/3

log₃(∛9) = log₃(3²⁽³) = 2/3

log₃(9/⁴√3) = log₃(3²/3¹⁽⁴) = log₃(3²⁻¹⁽⁴) = log₃(3⁷⁽⁴) = 7/4

log₃(3^√3) = √3·log₃3 = √3

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2)  2 ; 4 ; 1 ; 1/2 ; 1/4 ; 1/2√2 ; 4√2  in baza 2

log₂2 = 1

log₂4 = log₂2² = 2·log₂2 = 2

log₂1 = log₂2⁰ = 0·log₂2 = 0

log₂(1/2) = log₂(2⁻¹) = (-1)·log₂2 = -1

log₂(1/4) =  log₂(2⁻²) = (-2)·log₂2 = -2

log₂ (1/2√2) = log₂(1/√8) = log₂(8⁻¹⁽²) = log₂(2⁻³⁽²) = -3/2

log₂(4√2) = log₂(2²⁺¹⁽²) = log₂(2⁵⁽²) = 5/2