Question

Resolva a Equação exponencial:
$x = { \sqrt{5} }^{4} + \frac{1}{25} + 125$

Answer 1

Olá!

Temos:

$x\:=\:\:\:\sqrt{5}\:^4\:\:+\:\:\dfrac{1}{25}\:\:+\:125$

Resolvendo:

$x = \left(\sqrt{5}\right)^4+\dfrac{1}{25}+125$

$x = 5^2+\dfrac{1}{25}+125$

$x = 25+\dfrac{1}{25}+125$

aplicamos o mínimo múltiplo comum, temos:

$\dfrac{25x}{25\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}} = \dfrac{625}{25\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}} +\dfrac{1}{25\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}}+\dfrac{3125}{25\!\!\!\!\!\!\!\dfrac{\hspace{0.4cm}}{~}}$

$25x = 625 + 1 + 3125$

$25x = 3751$

$x = \dfrac{3751}{25}$

$\boxed{\boxed{x = 150.04}}\end{array}}\qquad\checkmark$

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Espero ter ajudado, Dexteright02! =)