Question

determinar a solução da equação exponencial (10^×)^×-1=(1/10)^6​

Answer 1

Resposta:

$x'= \frac{1+\sqrt{23} }{2}\\\\x"=\frac{1-\sqrt{23} }{2}$

Explicação passo-a-passo:

$(10^x)^{x-1} =(\frac{1}{10})^6\\10^{x^2-x}=10^{-6}\\x^2-x=-6\\\\x^2-x+6=0\\\\\Delta=b^2-4*a*c\\\Delta=(-1)^2-4*1*6\\\Delta=23\\\\x=\frac{-b\frac{+}{-}\sqrt{\Delta} }{2*a} \\\\x=\frac{1\frac{+}{-}\sqrt{23} }{2} =\\ \\x'= \frac{1+\sqrt{23} }{2}\\\\x"=\frac{1-\sqrt{23} }{2}$