Answer
$x=-\dfrac{\log7+4\log3}{\log3-2\log7}\approx2.27$
Work Step by Step
$3^{x+4}=7^{2x-1}$
Apply $\log$ to both sides of the equation:
$\log3^{x+4}=\log7^{2x-1}$
Take the exponents to multiply in front of each $\log$:
$(x+4)\log3=(2x-1)\log7$
Evaluate the products on both sides:
$x\log3+4\log3=2x\log7-\log7$
Take $2x\log7$ to the left side and $4\log3$ to the right side:
$x\log3-2x\log7=-\log7-4\log3$
Take common factor $x$ from the left side:
$x(\log3-2\log7)=-\log7-4\log3$
Take $\log3-2\log7$ to divide the right side:
$x=\dfrac{-\log7-4\log3}{\log3-2\log7}$
$x=-\dfrac{\log7+4\log3}{\log3-2\log7}\approx2.27$
