How would you make the equation $64\left(\frac 47\right)^{2x}=343$ so that it has a common base? I understand how to solve it using logs but could anyone show me how to solves it by making the numbers into common bases, thanks.
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Hint: can you factor 343 and 64? – Nov 22 '16 at 03:01
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Yes, i can factor 343 into 7^3 and 64 into either 2^6, 4^3 or 8^2, but it still wouldn't leave me with a common base, right? – D.Ademaj Nov 22 '16 at 03:06
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HINT:
As $64=4^3,343=7^3$
$$\dfrac{343}{64}=\left(\dfrac74\right)^3=\left(\dfrac47\right)^{-3}$$
Now $x^a=x^b\implies$
either $x=1$
or $x=0; a,b>0$
or $x=-1,a-b$ is even
or $a=b$
lab bhattacharjee
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