Answer
x = 2
Work Step by Step
Since $49 = 7^2$ we can multiply the exponent of the 49 hand side by $2$ while reducing the base to $7$.
The new equation is $7^{3x+4}= 7^{2(2x+1)}$.
Distributing the $2$ gives,
$7^{3x+4}= 7^{4x+2}$
We can now use Key Concept Algebra on pg. 515 stating If b is a positive number other than 1, then $b^x $ $= b^y$
if and only
if $x = y$.
Thus $ 3x+4 = 4x+2$
After moving the variables to one side and the constants to the other,
$ -2 = -x $ or $x=2$
