Answer
$x=\dfrac{\sqrt{10}}{10}\approx 0.3162$
Work Step by Step
Divide $2$ to both sides:
$\log_{10}x=-\dfrac{1}{2}$
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=10, y=-1/2, x=x$), we get:
$10^{-1/2}=x$
$x=\dfrac{1}{\sqrt{10}}$
$x=\dfrac{\sqrt10}{10}\approx 0.3162$
We confirm that the answer works:
$2\log_{10}{\left(\frac{\sqrt{10}}{10}\right)}=-1$
$2\cdot (-0.5)=-1$
$-1=-1$
