IMAT 2020 Q56 [Problem solving]

In order to solve this, we need to simplify the function in powers of 2:

8^{2x+3}\cdot \frac{1}{4^{3x}}= 2^{x+3} \to (2^3)^{2x+3}\cdot \frac{1}{(2^2)^{3x}}= 2^{x+3} \to 2^{3(2x+3)}\cdot \frac{1}{2^{2(3x)}}= 2^{x+3} \to
\to 2^{6x+9}\cdot 2^{-6x}= 2^{x+3}\to 2^{6x+9-6x}= 2^{x+3}\to 2^{+9} =2^{x+3}

From this, we get: 9 = x+3 \to x= 9-3 \to x=6

So the correct solution is (C) 6

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