Chapter 9 - Review - Page 598: 120

$x=\dfrac{1}{2}$

Express both sides of the equation with the same base. Once the bases are the same, then equate the exponents. That is, \begin{array}{l} 7^{4x}=49\\\\ 7^{4x}=7^2\\\\ 4x=2\\\\ x=\dfrac{2}{4}\\\\ x=\dfrac{1}{2} .\end{array}