Q.Solve for $x$: $3^{x+1} = 81$.

Rewrite the right-hand side as a power of the same base as the left, then equate the exponents.

Rewrite $81$ as a power of $3$ (the same base as the left side):

So the equation becomes:

Since both sides now share the same base, equate the exponents:

$x+1 = 4 \ \Rightarrow\ x = 3$ …

Miscounting how many times $3$ multiplies into itself to reach $81$ (e.g. wrongly using $3^3=27$ or $3^5=243$ instead of the correct $3^4=81$), or forgetting to subtract $1 …