Question

Se ln a = 3, ln b =5 e ln c = 7 , calcule ㏑(\frac{a^{2}b^{3}}{c^{4}} ).

Answer 1

Olá.

Usaremos as propriedades de logaritmos:

$\ell n(a\cdot b) = \ell n (a) + \ell n(b)\\ \\ \ell n(a/b) = \ell n(a) - \ell n (b)\\ \\ \ell n (a^n) = n\cdot \ell n (a)$

Com isso, escrevemos:

$\ell n\left(\dfrac{a^2 b^3}{c^4}\right) = \ell n(a^2b^3) - \ell n(c^4) =\\ \\ \\ =\ell n(a^2) + \ell n(b^3)-\ell n(c^4) = 2\cdot\ell n(a) + 3\cdot\ell n(b) - 4\ell n(c)=\\ \\ \\ = 2\cdot3 + 3\cdot 5-4\cdot7 = 6 + 15 - 28 = -7\\ \\ \\ \\ \therefore \ell n\left(\dfrac{a^2 b^3}{c^4}\right) = -7$