Question
Fill in the blank.
If $9 \times 3^n=3^6$, then $n=$ .......... .
If $9 \times 3^n=3^6$, then $n=$ .......... .
✓
Answer
If $9 \times 3^n=3^6$, then $n=\underline{4}$.
Solution:
$\text { If } 9 \times 3^n=3^6$
$\Rightarrow 3^2 \times 3^n=3^6$
$\Rightarrow 3^{(2+n)}=3^6$
Equating the powers:
$\Rightarrow(2+n)=6$
$\Rightarrow n=(6-2)=4$
Solution:
$\text { If } 9 \times 3^n=3^6$
$\Rightarrow 3^2 \times 3^n=3^6$
$\Rightarrow 3^{(2+n)}=3^6$
Equating the powers:
$\Rightarrow(2+n)=6$
$\Rightarrow n=(6-2)=4$
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