Question

Si log 2 ≈ 0,3 y log 3 ≈ 0,48, (≈ significa “aproximadamente igual”) aplica las propiedades de multiplicación y división y da un valor aproximado para: a) log6 b) log 1,5 c) log (4/3)

Answer 1

Propiedades de logaritmos.

Datos

$log(2) = 0.3 \\ log(3) = 0.48$

Propiedades

$log(ab) = log(a) + log(b) \\ log( \frac{a}{b} ) = log(a) - log(b)$

Resolviendo

Inciso a

$log(6) = log(6) \\ log(6)= log(3 \times 2) \\log(6) = log(3) + log(2) \\ log(6) = 0.48+ 0.3 \\ log(6) = 0.78$

Inciso b

$log(1.5) = log(1.5) \\ log(1.5) = log( \frac{3}{2} ) \\ log(1.5) = log(3) - log(2) \\ log(1.5) = 0.48 - 0.3 \\ log(1.5) = 0.18$

Inciso c

$log( \frac{4}{3}) = log( \frac{4}{3}) \\ log( \frac{4}{3}) = log(4) - log(3) \\ log( \frac{4}{3} ) = log(2 \times 2) - log(3) \\ log( \frac{4}{3} ) = log(2) + log(2) - log(3) \\ log( \frac{4}{3} ) = 0.3 + 0.3 - 0.48 \\ log( \frac{4}{3} ) = 0.6 - 0.48 \\ log( \frac{4}{3} ) = 0.12$