Chapter 7 - Exponential and Logarithmic Functions - 7-6 Natural Logarithms - Practice and Problem-Solving Exercises - Page 483: 72

$x=4$

Note that: $6561=3^8$ Thus, the given equation is equivalent to: $3^{2x}=3^8$ Use the rule $a^m=a^n \longrightarrow m=n$ to obtain: \begin{align*} 3^{2x}&=3^8\\\\ 2x&=8\\\\ \frac{2x}{2}&=\frac{8}{2}\\\\ x&=4 \end{align*}