Question

giúp mình với mai phải học rùi

2\(^{x+1}\)+2\(^{x+2}\)+2\(^{x+3}\)=448

tìm x \(\in\) Q

Answer 1

\(2^{x+1}+2^{x+2}+2^{x+3}=448\)

=>\(2^x.2+2^x.4+2^x.8=448\)

=>\(2^x\left(2+4+8\right)=448\)

=>\(2^x=32\)

=>\(2^x=2^5\)

=>\(x=5\)

Vậy...

Answer 2

ta có : \(2^{x+1}+2^{x+2}+2^{x+3}=448\) \(\Leftrightarrow2^{x+1}\left(1+2+2^2\right)=448\)

\(\Leftrightarrow2^{x+1}\left(1+2+4\right)=448\Leftrightarrow2^{x+1}.7=448\Leftrightarrow2^{x+1}=\dfrac{448}{7}\)

\(\Leftrightarrow2^{x+1}=64\Leftrightarrow2^{x+1}=2^6\Rightarrow x+1=6\Leftrightarrow x=6-1=5\)

vậy \(x=5\)

Answer 3

\(2^{x+1}+2^{x+2}+2^{x+3}=448\)

\(\Leftrightarrow2^x.2+2^x.2^2+2^{^{ }x}.2^3=448\)

\(\Leftrightarrow2^x.2+2^{^{ }x}.4+2^x.8=448\)

\(\Leftrightarrow2^x.\left(2+4+8\right)=448\)

\(\Leftrightarrow2^x.14=448\)

\(\Leftrightarrow2^x=448:14\)

\(\Leftrightarrow2^x=32=2^5\)

\(\Leftrightarrow x=5\)(do x \(\ne\pm1;0\))

Vậy .....

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