Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{2019}^{x+x+3}=2019\]
Simplify \(x+x+3\) to \(2x+3\).
\[{2019}^{2x+3}=2019\]
Use Definition of Common Logarithm: \({b}^{a}=x\) if and only if \(log_b(x)=a\).
\[2x+3=\log_{2019}{2019}\]
Use Change of Base Rule: \(\log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}\).
\[2x+3=\frac{\log{2019}}{\log{2019}}\]
Cancel \(\log{2019}\).
\[2x+3=1\]
Subtract \(3\) from both sides.
\[2x=1-3\]
Simplify \(1-3\) to \(-2\).
\[2x=-2\]
Divide both sides by \(2\).
\[x=-1\]
x=-1
