Question

tìm x biết \(2^{3x+2}=4^{x+5}\) 

giải chi tiết giùm mik nha

Answer 1

2^3x+2=4^x+5

2^2x+x.2²=4^x.4⁵

2^2x.2^x.2²=2^2x.2¹⁰

2^2x.2^x.2²-2^2x.2².2⁸=0

2^2x.2²(2^x-2⁸)=0

2^x-2⁸=0

2^x=2⁸

=>x=8

Answer 2

\(2^{3x+2}=4^{x+5}\Rightarrow2^{3x}.2^2=4^x.4^5\Rightarrow2^{3x}.2^2=\left(2^2\right)^{^x}.\left(2^2\right)^{^5}\Rightarrow2^{3x}.2^2=2^{2x}.2^{2.5}\Rightarrow2^{3x}:2^{2x}=2^{10}:2^2\Rightarrow2^{3x-2x}=2^{10-2}\Rightarrow2^x=2^8\Rightarrow x=8\)