Question

Resolva as equações exponenciais alguém pode me ajudar ?

Answer 1

Propriedades utilizadas:

$\rightarrow~\sqrt[b]{a^c}=a^{\frac{c}{b}}\\\\\rightarrow~\left(a^b\right)^c=a^{bc}\\\\\\\left(\frac{1}{1000}\right)^{2x+5}=\sqrt{10}\\\\\\\left(1000^{-1}\right)^{2x+5}=10^{\frac{1}{2}}\\\\\\\left(\left(10^3\right)^{-1}\right)^{2x+5}=10^{\frac{1}{2}}\\\\\\\left(10^{-1~.~3}\right)^{2x+5}=10^{\frac{1}{2}}\\\\\\\left(10^{-3}\right)^{2x+5}=10^{\frac{1}{2}}\\\\\\10^{-3.(2x+5)}=10^{\frac{1}{2}}\\\\\\10^{-6x-15}=10^{\frac{1}{2}}\\\\\\-6x-15=\frac{1}{2}\\\\\\-6x=\frac{1}{2}+15$

$-6x=\frac{31}{2}\\\\\\x=-\frac{31}{2~.~6}\\\\\\\boxed{x=-\frac{31}{12}}$

Resposta:   x = -31/12