Answer
$x=\dfrac{7}{2}$
Work Step by Step
RECALL:
$\log_a{x} = y \longrightarrow a^y=x$
Use the definition above to obtain:
$\log_2{(2x+1)}=3
\\
\longrightarrow 2^3=2x+1
\\8=2x+1$
Subtract 1 on both sides of the equation to obtain:
$\begin{array}{ccc}
&8-1 &= &2x+1-1
\\&7 &= &2x\end{array}$
Divide 2 on both sides of the equation to obtain:
$\frac{7}{2}=\frac{2x}{2}
\\\frac{7}{2}=x$