Question

determine o valor de X em cada expressão, na imagem​

Answer 1

$\boxed{\begin{array}{l}\rm Determine~o~valor~de~x~em~cada~express\tilde ao.\\\tt a)~\rm\sqrt[\rm12]{\rm2^8}=\sqrt[\rm x]{\rm 2^3}\\\\\tt b)~\rm\sqrt[\rm8]{\rm\dfrac{2041}{625}}=\sqrt[\rm x]{\rm\dfrac{7}{5}} \end{array}}$

$\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao:}\\\tt a)~\sf\sqrt[\sf12]{2^8}=\sqrt[\sf x]{\sf 2^3}\\\sf 2^{\frac{8}{12}}=2^{\frac{3}{x}}\\\sf\dfrac{8}{12}=\dfrac{3}{x}\\\\\sf8x=36\\\sf x=\dfrac{36\div4}{8\div4}\\\\sf x=\dfrac{9}{2}\end{array}}$

$\boxed{\begin{array}{l}\tt b)~\sf\sqrt[\sf 8]{\sf\dfrac{2041}{625}}=\sqrt[\sf x]{\sf\dfrac{7}{5}}\\\sf\bigg(\dfrac{2041}{625}\bigg)^{\frac{1}{8}}=\bigg(\dfrac{7}{5}\bigg)^{\frac{1}{x}}\\\sf\ell n\bigg(\dfrac{2041}{625}\bigg)^{\frac{1}{8}}=\ell n\bigg(\dfrac{7}{5}\bigg)^{\frac{1}{x}}\\\sf\dfrac{1}{8}\ell n\bigg(\dfrac{2041}{625}\bigg)=\dfrac{1}{x}\ell n\bigg(\dfrac{7}{5}\bigg)\\\\\sf x=\dfrac{8\ell n\bigg(\frac{7}{5}\bigg)}{\ell n\bigg(\frac{2041}{625}\bigg)}\end{array}}$