Question

sabenddo-se que:log a =8, log b=2 e log c=1,calcular log ( ∛a² / b²·c)

Answer 1

$log~(\dfrac{\sqrt[3]{a^{2}}}{b^{2}c})=log~\sqrt[3]{a^{2}}-log~b^{2}-log~c\\\\\\log~(\dfrac{\sqrt[3]{a^{2}}}{b^{2}c})=log~a^{(2/3)}-2*log~b-log~c\\\\\\log~(\dfrac{\sqrt[3]{a^{2}}}{b^{2}c})=(2/3)*log~a-2*log~b-log~c\\\\\\log~(\dfrac{\sqrt[3]{a^{2}}}{b^{2}c})=(2/3)*8-2*2-1$

$log~(\dfrac{\sqrt[3]{a^{2}}}{b^{2}c})=(16/3)-4-1\\\\\\log~(\dfrac{\sqrt[3]{a^{2}}}{b^{2}c})=(16/3)-5\\\\\\log~(\dfrac{\sqrt[3]{a^{2}}}{b^{2}c})=(16-15)/3\\\\\\\boxed{\boxed{log~(\dfrac{\sqrt[3]{a^{2}}}{b^{2}c})=\dfrac{1}{3}}}$