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The question is:

Given that there is more than one value of $x$ to the question $4^{ax} = b \times 8^x$, find all possible values of $a$ and $b$.

I know that you can use logs to solve this question, but are there any other methods? (like deductions or something like that?)

Thanks!

kwhk
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  • It is simple $2^{2ax}=b2^{3x}$, hence, $b$ must be an power of $2$. Say $b=2^k$, then $k$ must be odd, so $b=2^{2m+1}$, hence we get $2ax=2m+1+3x$. Now, solve from here. –  Oct 05 '15 at 15:13
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    You could tell this in answers. Whatever it may be, of course it is not a comment. – uniquesolution Oct 05 '15 at 15:39

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