Answer
$x=1$
Work Step by Step
We are given the exponential equation $3^{2x+1}=27$.
We can express each side using a common base and then solve for $x$.
$3^{2x+1}=3^{3}=27$
Take the natural log of both sides.
$ln(3^{2x+1})=ln(3^{3})$
$(2x+1)ln(3)=3ln(3)$
Divide both sides by $ln(3)$.
$2x+1=3$
Subtract 1 from both sides.
$2x=2$
Divide both sides by 2.
$x=1$
