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Product Law

If 3 x +27 ...

Question

If $3^{x} + 27 (3^{- x}) = 12$ , then what is the value of $x$ ?

1

only

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2

only

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1

2

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0

1

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Solution

The correct option is D $1$ or $2$
Since, $3^{x} + 27 (3^{- x}) = 12 \Rightarrow 3^{2 x} + 27 = (12) 3^{x}$
$\Rightarrow (3^{x})^{2} - (12) 3^{x} + 27 = 0 \Rightarrow (3^{x} - 9) (3^{x} - 3) = 0$
$\Rightarrow 3^{x} = 9$ & $3^{x} = 3 \Rightarrow x = 1, 2$

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