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Indices (Exponents) — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSIndices (Exponents)2 Marks
Question
Solve for $x : 9^{x+2}= 720 + 9^x$
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Answer

$9^{x+2}= 720 + 9^x$
$\Rightarrow 9^{x+2}- 9^x= 720$
$\Rightarrow 9^x(9^2- 1) = 720$
$\Rightarrow 9^x(81 - 1) = 720$
$\Rightarrow 9^x(80) = 720$
$\Rightarrow 9^x= 9$
$\Rightarrow 9^x= 9^1$
$\Rightarrow x = 1$

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