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Indices — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSIndices3 Marks
Question
Solve for $x:9^{x+4}= 3^2 x (27)^{x+1}$
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Answer

$9^{x+4}=3^2 \times(27)^{x+1}$
$ \Rightarrow 9^{x+4}=3^2 \times\left(3^3\right)^{x+1}$
$ \Rightarrow 3^{2(x+4)}=3^2 \times 3^{3 x+3} $
$ \Rightarrow 3^{2 x+8}=3^{2+3 x+3} $
$\Rightarrow 2 x+8=2+3 x+3 $
$ \Rightarrow 2 x+8=3 x+5 $
$ \Rightarrow x=3$

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