Question

sabendo que loga A=2 . loga C- 1/3 . loga d calcule A em função de d​

Answer 1

Vamos usar as seguintes propriedades de Log :

$\displaystyle 1) \ \text n.\text{log }_\text {x } \text y = \text{log }_\text{x }\text y^{ \text n} \\\\ 2) \ \text{log}_\text{x } \text y-\text{log}_\text{x }\text z = \text{log}_\text{x }(\frac{\text y}{\text z} )$

Temos:

$\displaystyle \text{log }_\text {a } \text A =2.\text{log }_ \text {a }\text c - \frac{1}{3}.\text{log}_\text{a }\text d \\\\\\ \text{log }_\text{a }\text A = \text{log }_\text{a }\text c^2-\text{log }_\text{a }\sqrt[3]{\text d} \\\\\\ \text{log }_\text{a }\text A=\text{log }_\text{a }[\ \frac{\text c^2}{\sqrt[3]{\text d}}\ ] \\\\\\ \huge\boxed{\ \text A = \frac{\text c^2}{\sqrt[3]{\text d}}\ }\checkmark$