Chapter 5 - Exponential and Logarithmic Functions - 5.4 Logarithmic Functions - 5.4 Assess Your Understanding - Page 296: 91

$x=\frac{7}{2}$

We know that if $\log_a y=x$ then $a^x=y$. Hence, if $\log_2{(2x+1)}=3$, then $2^3=2x+1$. Solve the equation above to obtain: \begin{align*} 2^3&=2x+1\\ 8&=2x+1\\ 8-1&=2x+1-1\\ 7&=2x\\ \frac{7}{2}&=\frac{2x}{2}\\ \frac{7}{2}&=x \end{align*}