Question: "Solve: 9x=3x−1"

King Waters

Answered question

2022-12-31

Solve:

9^{x} = 3^{x - 1}

Adelyn French

Beginner2023-01-01Added 8 answers

\leq f t s i d e = 9^{x} = {(3^{2})}^{x} = 3^{2 x}

\Rightarrow 3^{2 x} = 3^{x - 1} \leftarrow e q u a t i o n \to b e s o l v e d

Since the bases are equal. That is both 3, then we can equate the exponents.

\Rightarrow 2 x = x - 1 \Rightarrow x = - 1

A s a c h e c k

Put this value into the equation, and the answer will be the one where the left and right sides of the equation are equal.

\leq f t s i d e = 9^{- 1} = \frac{1}{9}

r i g h t s i d e = 3^{- 2} = \frac{1}{3^{2}} = \frac{1}{9}

\Rightarrow x = - 1 i s t h e s o l u t i o n

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