solve: $9^{x - 3}=729$

Explanation:

Step1: Rewrite 729 as a power of 9

Since $9^3=729$, the equation $9^{x - 3}=729$ can be rewritten as $9^{x - 3}=9^3$.

Step2: Equate the exponents

If $a^m=a^n$, then $m = n$ for $a>0,a\neq1$. So, $x - 3=3$.

Step3: Solve for x

Add 3 to both sides of the equation $x - 3=3$. We get $x=3 + 3$. $x=6$

Answer:

$6$