https://olm.vn/hoi-dap/question/127526.html
MK viết lại ,bn xem đề thế này có đg ko nhé
\(a,\dfrac{1}{9}.3^4.3^{n+1}=9^4\)
\(b,\dfrac{1}{2}.2^{n+4}.2^n=9.2^5\)
2:
\(A=2^0+2^1+2^2+...+2^{2010}+2^{2012}\) và \(B=2^{2012}\)
Ta có :
MK theeys đề b2 này cứ sai sai
\(A=2^0+2^1+2^2+...+2^{2010}+2^{2012}\) \(\Rightarrow2A=2\left(2^0+2^1+2^2+...+2^{2010}+2^{2012}\right)\) \(\Rightarrow2A=2+2^2+2^3+...+2^{2011}+2^{2013}\) \(\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2011}+2^{2013}\right)-\left(1+2+2^2+...+2^{2010}+2^{2012}\right)\) \(\Rightarrow A=2+2^2+2^3+...+2^{2011}+2^{2013}-1-2-2^2-...-2^{2010}-2^{2012}\) \(\Rightarrow A=2^{2013}-1\)
B1:
\(a,\dfrac{1}{9}.3^4.3^{n+1}=9^4\)
\(\Rightarrow\dfrac{1}{9}.3^{n+5}=9^4\)
\(\Rightarrow3^{n+5}=\dfrac{9^4}{\dfrac{1}{9}}\)
\(\Rightarrow3^{n+5}=9^4.9\)
\(\Rightarrow3^{n+5}=9^5\)
\(\Rightarrow3^{n+5}=\left(3^2\right)^5\)
\(\Rightarrow3^{n+5}=3^{10}\Rightarrow n+5=10\Rightarrow n=5\)
\(b,\dfrac{1}{2}.2^{n+4}.2^n=9.2^5\)
\(\Rightarrow\dfrac{1}{2}.2^{2n+4}=9.2^5\)
\(\Rightarrow2^{2n+4}=\dfrac{9.2^5}{\dfrac{1}{2}}\)
\(\Rightarrow2^{2n+4}=9.2^5.2\)
\(\Rightarrow2^{2n+4}=9.2^6\Rightarrow2^{2n}.16=9.2^6\)
\(\Rightarrow2^{2n}=\dfrac{9.2^6}{2^4}\Rightarrow2^{2n}=9.2^2\)
\(\Rightarrow2^{2n}=6^2\)
