Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

It follows that $3^{y} = 3^{2x}$

But $3^{2x} \equiv (3^{x})^{2} \equiv (3^{2})^{x}$ (I think? Since e.g. $(x^{2})^{3} \equiv x^{2 \cdot 3} \equiv (x^{3})^{2}$ right?)

So which of the following is correct? $y = 2x$ or $y = x^2$ or $y = 2^x$?

Thanks!

share|improve this question
2  
Ahha! $y = 2x$ because this is the only one where the base is still 3, correct? –  Danny King May 22 '11 at 12:28
add comment

2 Answers 2

up vote 3 down vote accepted

$y=2x$ is correct. $(3^2)^x=3^y$ is also correct but does not imply $y=2^x$ or something similar.

The confusion might arise from the fact that powering is not associative: i.e. in general it is not true that $a^{(b^c)}=(a^b)^c$, e.g. $3^{(2^3)}\ne (3^2)^3$.

share|improve this answer
add comment

$y=2x$ is the correct option. Because if $$x^{a}=x^{b} \Longrightarrow a=b$$

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.