Question

Resolva a equação exponencial
(√3)×= 81

Answer 1

Resposta:

Explicação passo-a-passo:

 (√3)× = 81

  $3^\frac{1}{2} ^x = 3^{4}$  <--- bases iguais, iguala os expoentes

   $\frac{x}{2} = 4 ----> x = 8$

Answer 2

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$\boxed{\sf{\underline{Pot\hat{e}ncia~de~expoente~racional}}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{a^{\frac{m}{n}}=\sqrt[\sf n]{\sf a^\sf m}}}}}}$

$\sf{(\sqrt{3})^x=81}\\\sf{(3^{\frac{1}{2}})^x=81}\\\sf{3^{\frac{x}{2}}=81}$

$\begin{array}{c|l}\tt{81}&\tt{3}\\\tt{27}&\tt{3}\\\tt{9}&\tt{3}\\\tt{3}&\tt{3}\\\tt{1}\end{array}\\\sf{81=3^4}$

$\sf{3^{\frac{x}{2}}=3^4}\\\sf{bases~iguais~nos~fornece~expoentes~iguais}\\\sf{\dfrac{x}{2}=4}\\\sf{x=2\cdot4}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{x=8\checkmark}}}}}$