Simple Arithmetic

Solve for x:

${\displaystyle 3^{3x+1}=81}$

Step 1: Represent 81 exponentially with a base of 3

${\displaystyle 3\cdot <!--\; \cdot \; -->3\cdot <!--\; \cdot \; -->3\cdot <!--\; \cdot \; -->3=81}$, therfore ${\displaystyle 3^4=81}$

Step 2: Set the exponents equal to each other and solve for x

${\displaystyle 3^{3x+1}=3^4}$

${\displaystyle 3x+1=4}$

${\displaystyle 3x=3}$

${\displaystyle x=1}$