\(a,3^{x+2}-3^{x+1}=162\\ 3^{x+1}\left(3-1\right)=162\\ 3^{x+1}.2=162\\ 3^{x+1}=162:2=81\\ 3^{x+1}=3^4\\x+1=4\\ x=4-1=3 \)
\(b,5^{x+1}+5^{x+2}=3750\\ 5^{x+1}\left(1+5\right)=3750\\ 5^{x+1}.6=3750\\ 5^{x+1}=3750:6=625\\ 5^{x+1}=5^5\\ x+1=5\\ x=5-1=4\)
a.
\(3^{x+2}-3^{x+1}=162\\ \Rightarrow3^{x+1}\left(3^1-1\right)=162\\ \Rightarrow3^{x+1}.2=162\\ \Rightarrow3^{x+1}=81\\ \Rightarrow x+1=4\\ \Rightarrow x=3\)
b.
\(5^{x+1}+5^{x+2}=3750\\ \Rightarrow5^{x+1}\left(1+5\right)=3750\\ \Rightarrow5^{x+1}=625\\ \Rightarrow x+1=4\\ \Rightarrow x=3\)
Câu khác TT
\(a,3^{x+2}-3^{x+1}=162\)
\(\Leftrightarrow3^x\left(3^2-3\right)=162\)
\(\Leftrightarrow3^x.6=162\)
\(\Leftrightarrow3^x=27\)
\(\Leftrightarrow3^x=3^3\)
\(\Leftrightarrow x=3\)
Vậy ..........
\(b,5^{x+1}+5^{x+2}=3750\)
\(\Leftrightarrow5^x\left(5+5^2\right)=3750\)
\(\Leftrightarrow5^x.30=3750\)
\(\Leftrightarrow5^x=125\)
\(\Leftrightarrow5^x=5^3\)
\(\Leftrightarrow x=3\)
Vậy ...............
\(a,3^{x+2}-3^{x+1}=162.\)
\(3^x.3^2-3^x.3^1=162.\)
\(3^x\left(3^2-3^1\right)=162.\)
\(3^x.6=162.\)
\(3^x=\dfrac{162}{6}.\)
\(3^x=27.\)
\(3^x=3^3\Rightarrow x=3.\)
Vậy.....
\(b,5^{x+1}+5^{x+2}=3750.\)
\(5^x.5+5^x.5^2=3750.\)
\(5^x\left(5+5^2\right)=3750.\)
\(5^x.30=3750.\)
\(5^x=\dfrac{3750}{30}.\)
\(5^x=125.\)
\(5^x=5^3\Rightarrow x=3.\)
Vậy.....
\(c,7^{4-x}-7^{3-x}=294.\)
\(7^4:7^x-7^3:7^x=294.\)
\(\left(7^4-7^3\right):7^x=294.\)
\(2058:7^x=294.\)
\(7^x=\dfrac{2058}{294}.\)
\(7^x=7.\)
\(7^x=7^1\Rightarrow x=1.\)
Vậy.....
\(d,11^x-11^{x-1}=1452.\)
\(11^x:1-11^x:11=1452.\)
\(11^x:\left(1-11\right)=1452.\)
\(11^x:\left(-10\right)=1452.\)
\(11^x=1452.\left(-10\right).\)
\(11^x=-14250.\)
\(\Rightarrow x\in\varnothing.\)
Vậy.....
\(e,2^x+2^{x-2}=40.\)
\(2^x+2^x:2^2=40.\)
\(2^x:\left(1+2^2\right)=40.\)
\(2^x:5=40.\)
\(2^x=40.5.\)
\(2^x=200.\)
\(\Rightarrow x\in\varnothing.\)
Vậy.....
