Chapter 5 - Exponential and Logarithmic Functions - 5.4 Logarithmic Functions - 5.4 Assess Your Understanding - Page 296: 98

$x=2$

We know that by definition then $log_a {y}=x$, then $y=a^x$. Hence if $log_3 {(243)}=2x+1$, then $3^{2x+1}=343=3^5$. The base is the same on the two sides of the equation, hence the exponents must be equal. Solve the equation above to obtain: \begin{align*}5=2x+1\end{align*} \begin{align*}4=2x\end{align*} \begin{align*}x=2\end{align*}