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# help

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If $$3^x = 27^{y - 5}$$ and $$2^y = 8^{2x - 4}$$, then find y - x.

May 31, 2020

#1
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Note that $$27=3^3 \text{ and } 8=2^3$$

So  $$3^x = 3^{3(y-5)} \text{ and }2^y=2^{3(2x-4)}$$

Now equate powers so that you have two equations for x and y:

x = 3(y - 5)   and   y = 3(2x - 4)

Can you take it from here?

Jun 1, 2020