Question

Sabendo que log a = 8 log b = -1 log c = 5 calcule o valor de log ( a^2 b^3/c).

Answer 1

$\mathrm{\log{a}=8\ \ \|\ \ \log{b}=-1\ \ \|\ \ \log{c}=5}\\\\ \mathrm{*\ Lembrando\ que:}\ \ \boxed{\mathrm{\log{x^n}=n.\log{x}}}\\\\ \boxed{\mathrm{\log{(x.y)}=\log{x}+\log{y}}}\ \ \boxed{\mathrm{\log{\bigg(\dfrac{x}{y}\bigg)}=\log{x}-\log{y}}}\\\\\\ \mathrm{\log{\bigg(\dfrac{a^2.b^3}{c}\bigg)}=\log{(a^2.b^3)}-\log{c}=}\\\\ \mathrm{=\log{a^2}+\log{b^3}-\log{c}=2.\log{a}+3.\log{b}-\log{c}=}\\\\ \mathrm{=2.8+3.(-1)-5=16-3-5=\boxed{\mathbf{8}}}$