Question

equaçoes exponencias (1/1000)^2x+1=raiz de 10

Answer 1

(1/1000)^2x+1= V10
( 10^-3)^2x+1 =  10^1/2

-3(2x+1) = 1
                  2

-6(2x + 1 ) = 1

-12x - 6 = 1

12x = - 6 - 1

x = - 7/12

Answer 2

$\left(\dfrac{1}{1000}\right)^{2x+1}=\sqrt{10}\\\\\\(10^{0-3})^{2x+1}=10^{\frac{1}{2}}\\\\\\\left(\dfrac{10^0}{10^3}\right)^{2x+1}=10^{\frac{1}{2}}\\\\\\(10^{-3})^{2x+1}=10^{\frac{1}{2}}\\\\10^{-6x-3}=10^{\frac{1}{2}}\\\\\therefore\\\\-6x-3=\dfrac{1}{2}\\\\\\-6x=\dfrac{1}{2}+3\\\\\\-6x=\dfrac{7}{2}\\\\\\x=\dfrac{7}{-6\cdot2}\\\\\\x=-\dfrac{7}{12}\\\\\\\\\boxed{S=\left\{-\dfrac{7}{12}\right\}}$