\(\dfrac12\cdot2^{x+4}\cdot2^x=2^5\\\Rightarrow \dfrac{2^{x+4}\cdot2^x}{2}=2^5\\\Rightarrow 2^{x+4+x}=2^5\cdot2\\\Rightarrow 2^{2x+4}=2^6\\\Rightarrow 2x+4=6\\\Rightarrow 2x=6-4\\\Rightarrow2x=2\\\Rightarrow x=1\)
\(\dfrac{1}{2}\cdot2^x+4\cdot2^x=2^5\)
=>\(2^x\cdot\dfrac{9}{2}=2^5\)
=>\(2^x=32:\dfrac{9}{2}=\dfrac{64}{9}\)
=>\(x=log_2\left(\dfrac{64}{9}\right)\)
\(\dfrac{1}{2}\cdot2^x+4\cdot2^x=2^5\\\Rightarrow 2^x\cdot\Bigg(\dfrac12+4\Bigg)=32\\\Rightarrow2^x\cdot\dfrac92=32\\\Rightarrow2^x=32:\dfrac92\\\Rightarrow2^x=\dfrac{64}{9}\)
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