Jambmaths question:
If ${{27}^{x+2}}\div {{9}^{x+1}}={{3}^{2x}}$, find x
Option A:
3
Option B:
4
Option C:
5
Option D:
6
Jamb Maths Solution:
$\begin{align} & {{27}^{x+2}}\div {{9}^{x+1}}={{3}^{2x}} \\ & \frac{{{27}^{x+2}}}{{{9}^{x+1}}}={{3}^{2x}} \\ & \frac{{{3}^{3(x+2)}}}{{{3}^{2(x+1)}}}={{3}^{2x}} \\ & {{3}^{3(x+2)-2(x+1)}}={{3}^{2x}} \\ & \text{Equating the powers since the bases are equal} \\ & 3(x+2)-2(x+1)=2x \\ & 3x+6-2x-2=2x \\ & x+4=2x \\ & x=4 \\\end{align}$
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