Indices confusion

Consider the formula $3^{y} = 9^{x}$

It adheres to that $3^{y} = 3^{2x}$

But $3^{2x} \equiv (3^{x})^{2} \equiv (3^{2})^{x}$ (I assume? Given that as an example $(x^{2})^{3} \equiv x^{2 \cdot 3} \equiv (x^{3})^{2}$ right?)

So which of the adhering to is proper? $y = 2x$ or $y = x^2$ or $y = 2^x$?

Many thanks!

1
2022-06-07 14:33:03
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Answers: 2

$y=2x$ is the proper alternative. Due to the fact that if $$x^{a}=x^{b} \Longrightarrow a=b$$

2
2022-06-07 14:59:01
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$y=2x$ is proper. $(3^2)^x=3^y$ is additionally proper yet does not indicate $y=2^x$ or something comparable.

The complication could emerge from the reality that powering is not associative: i.e. as a whole it is not real that $a^{(b^c)}=(a^b)^c$, e.g, $3^{(2^3)}\ne (3^2)^3$

3
2022-06-07 14:58:56
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