Question

Solve for $x$ in the equation $3^{(2+x)}+3^{(1+x)}=2916.$
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Answer 1

We have $3^{(2+x)}+3^{(1+x)}=2916.$
$\Rightarrow 3^2\times 3^x+3^1\times 3^x=2916$
$\because a^{m+n}=a^m\times a^n$
i.e., $9\times 3^x+3\times 3^x=2916$
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$\Rightarrow 3^x(9+3)=2916$
$\Rightarrow 3^x=\frac{2916}{12}=243$
$\Rightarrow 3^x=3^5$
Since the powers on both sides have equal bases, they must have equal exponents as well.
$\therefore x=5$
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