King Waters

2022-12-31

Solve: ${9}^{x}={3}^{x-1}$

Expert

$\le ftside={9}^{x}={\left({3}^{2}\right)}^{x}={3}^{2x}$
$⇒{3}^{2x}={3}^{x-1}←equation\to besolved$
Since the bases are equal. That is both 3, then we can equate the exponents.
$⇒2x=x-1⇒x=-1$
$Asacheck$
Put this value into the equation, and the answer will be the one where the left and right sides of the equation are equal.
$\le ftside={9}^{-1}=\frac{1}{9}$
$rightside={3}^{-2}=\frac{1}{{3}^{2}}=\frac{1}{9}$
$⇒x=-1isthesolution$

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