Answer
$x=\dfrac{1}{60}\approx0.0167$
Work Step by Step
Add $3$ to both sides:
$\log_{10}{6x}-3+3=-4+3$
$\log_{10}{6x}=-1$
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=10, y=4, x=x$), we get:
$10^{-1}=6x$
$\dfrac{1}{10}=6x$
$x=\dfrac{1}{60}\approx0.0167$
We confirm that the answer works:
$\log_{10}{\left(6\cdot \frac{1}{60}\right)}-3=-4$
$\log_{10}{\left(\frac{1}{10}\right)}-3=-4$
$\log_{10}(10^{-1})-3=-4$
$-1-3=-4$
$-4=-4$
