Question

Se ㏒ a X=2 e ㏒ x Y=3 , então calcule ㏒ a $\sqrt[5]{x. y^{3} }$

Answer 1

$\log_a(\sqrt[5]{xy^3})=\\\\\dfrac{\log_a(xy^3)}{5}=\\\\\dfrac{\log_a(x)+\log_a(y^3)}{5}=\\\\\dfrac{\log_a(x)+3\log_a(y)}{5}=\\\\\dfrac25+\dfrac35\cdot\dfrac{\log_x(y)}{\log_x(a)}=\\\\\dfrac25+\dfrac35\cdot\dfrac{3}{\frac12}=\\\\\dfrac25+\dfrac35\cdot6=\dfrac25+\dfrac{18}{5}=\dfrac{20}{5}=4$