Question

calcule o valor de x em √((4\9)^(x-4)) = 1,5

Answer 1

$\large\boxed{\begin{array}{l}\sf 1,5=\dfrac{15\div5}{10\div5}=\dfrac{3}{2}\\\\\sf\sqrt{\bigg(\dfrac{4}{9}\bigg)^{x-4}}=1,5\\\\\sf\sqrt{\bigg(\dfrac{4}{9}\bigg)^{x-4}}=\dfrac{3}{2}\\\\\sf\bigg[\sqrt{\bigg(\dfrac{4}{9}\bigg)^{x-4}}\bigg]^2=\bigg(\dfrac{3}{2}\bigg)^2\\\\\sf\bigg(\dfrac{4}{9}\bigg)^{x-4}=\dfrac{9}{4}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf\bigg(\dfrac{4}{9}\bigg)^{x-4}=\bigg(\dfrac{4}{9}\bigg)^{-1}\\\\\sf x-4=-1\\\sf x=4-1\\\sf x=3\end{array}}$