a) \(3^{-2}.3^4.3^n=3^7\)
\(\Rightarrow3^{-2}.3^n=3^7:3^4\)
\(\Rightarrow3^{-2+n}=3^3\)
\(\Rightarrow-2+n=3\)
\(\Rightarrow n=3+2=5\)
Vậy \(n=5.\)
b) \(2^{-1}.2^n+4.2^n=9.2^5\)
\(\Rightarrow2^n\left(2^{-1}+4\right)=9.2^5\)
\(\Rightarrow2^n.9.\dfrac{1}{2}=9.2^5\)
\(\Rightarrow2^n.\dfrac{1}{2}=2^5\)
\(\Rightarrow2^n=2^5.2=2^6\)
\(\Rightarrow n=6.\)
Vậy \(n=6.\)
c) Nhìn cái đề mk chẳng hiểu gì hết, cái dấu sau dấu lớn là dấu gì thế???
a) \(3^{-2}\cdot3^4\cdot3^n=3^7\) (1)
\(\Leftrightarrow3^{n+2}=3^7\)
\(\Leftrightarrow n+2=7\)
\(\Leftrightarrow n=7-2\)
\(\Leftrightarrow n=5\)
Vậy tập nghiệm phương trình (1) là \(S=\left\{5\right\}\)
b) \(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\) (2)
\(\Leftrightarrow\left(2^{-1}+4\right)\cdot2^n=9\cdot2^5\)
\(\Leftrightarrow\left(\dfrac{1}{2}+4\right)\cdot2^n=9\cdot2^5\)
\(\Leftrightarrow\dfrac{9}{2}\cdot2^n=9\cdot2^5\)
\(\Leftrightarrow2^n=2^6\)
\(\Leftrightarrow n=6\)
Vậy tập nghiệm phương trình (2) là \(S=\left\{6\right\}\)
Giải:
a) \(3^{-2}.3^4.3^n=3^7\)
\(\Leftrightarrow3^{-2+4+n}=3^7\)
Vì \(3=3\)
\(\Rightarrow-2+4+n=7\)
\(\Rightarrow2+n=7\)
\(\Leftrightarrow n=7-2=5\)
Vậy \(n=5\)
c) \(2.16\ge2^n>4\)
\(\Leftrightarrow2.2^4\ge2^n>2^2\)
\(\Leftrightarrow2^5\ge2^n>2^2\)
\(\Rightarrow n\in\left\{3;4;5\right\}\)
Vậy \(n\in\left\{3;4;5\right\}\)
Chúc bạn học tốt!
a/ \(3^{-2}\cdot3^4\cdot3^n=3^7\)
\(\Rightarrow3^{-2+4+n}=3^7\)
\(\Rightarrow2+n=7\Rightarrow n=7-2=5\)
b/ \(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)
\(\Rightarrow2^n\left(2^{-1}+4\right)=288\)
\(\Rightarrow2^n=288:\dfrac{9}{2}=64=2^6\)
\(\Rightarrow n=6\)
c/ >_ là lớn hơn hoặc = hả bn?!
\(2\cdot16\ge2^n>4\)
hay \(2^5\ge2^n>2^2\)
=> \(n=\left\{3;4;5\right\}\)
nếu là: \(2\cdot16>2^n>4\)
\(\Rightarrow2^5>2^n>2^2\)
\(\Rightarrow n=\left\{3;4\right\}\)
\(3^{-2}.3^4.3^n=3^7\)
\(\Leftrightarrow3^{-2+4+n}=3^7\)
\(3^{2+n}=3^7\)
\(\Leftrightarrow2+n=7\Rightarrow n=5\)
\(2^{-1}.2^n+4.2^n=9.2^5\)
\(\dfrac{1}{2}.2^n+4.2^n=9.32\)
\(2^n\left(\dfrac{1}{2}+4\right)=288\)
\(2^n.4,5=288\)
\(2^n=288:4,5=64\Leftrightarrow n=6\)
\(2.16\ge2^n>4\)
\(\Leftrightarrow2.2^4\ge2^n>2^2\)
\(2^5\ge2^n>4\)
\(\Leftrightarrow5\ge n>2\Leftrightarrow n\in\left\{3;4;5\right\}\)
