Question

equação exponencial! por favor preciso dos cálculos! (tentei fazer caber a foto inteira, mas em caso de dúvidas o primeiro numero meio cortado é um 25!)​

Answer 1

Resposta:

x=2  ou  x=1

Explicação passo-a-passo:

$\dfrac{25^{x}+125}{6}=5^{x+1}\\\\(5^{2})^{x}+125=6.5^{x}.5^{1}\\\\(5^{x})^{2}+125=30.5^{x}\\\\(5^{x})^{2}-30.5^{x}+125=0\\\\Fazendo\\\\y=5^{x}\\\\\\teremos\\\\y^{2}-30y+125\\\\\\y=\dfrac{-(-30)\pm\sqrt{(-30)^{2}-4.1.125}}{2.1}\\\\\\ y=\dfrac{30\pm\sqrt{900-500}}{2}\\\\\\y=\dfrac{30\pm\sqrt{400}}{2}\\\\\\y=\dfrac{30\pm20}{2}\\\\\\y'=\dfrac{30+20}{2}=\dfrac{50}{2}=25\\\\\\y"=\dfrac{30-20}{2}=\dfrac{10}{2}=5\\\\para\\y=25\\\\5^{x}=25\\\\5^{x}=5^{2}\\\\x=2$

para

y=5

$5^{x}=5\\\\5^{x}=5^{1}\\\\\\x=1$