1, Tìm x :
a, \(x^7.x^5=3^{12}\)
\(\Rightarrow x^{12}=3^{12}\)
\(\Rightarrow x=3\)
Vậy x = 3
b, \(\left(x+1\right)^4=5^8\div25^4\)
\(\left(x+1\right)^4=5^8\div\left(5^2\right)^4\)
\(\left(x+1\right)^4=5^8\div5^8\)
\(\left(x+1\right)^4=1\)
\(\Rightarrow x\in\left\{0;1\right\}\)
Vậy \(x\in\left\{0;1\right\}\)
c, \(x^6=x\)
\(\Rightarrow x^6-x=0\)
\(\Rightarrow x.x^5-x.1=0\)
\(\Rightarrow x\left(x^5-1\right)=0\)
x = 0 hoặc x5 - 1 = 0
x = 0 hoặc x5= 1
x = 0 hoặc x5 = 1
\(\Rightarrow x\in\left\{0;1\right\}\)
Vậy \(x\in\left\{0;1\right\}\)
2, Tính :
\(\left(4^{20}+4^{15}\right)\div\left(4^{10}+4^5\right)\)
\(=4^{15}.\left(4^5+1\right)\div4^5.\left(4^5+1\right)\)
\(=4^{15}\div4^5\)
\(=4^{10}\)
Vậy giá trị biểu thức trên bằng 410
\(A=2^0+2^1+2^2+...+2^{2016}\)
\(2A=2+2^2+2^3+...+2^{2017}\)
\(2A-A=\left(2+2^2+2^3+...+2^{2017}\right)-\left(2^0+2^1+2^2+...+2^{2016}\right)\)
\(\Rightarrow A=2^{2017}-1\)
Vậy : \(A=2^{2017}-1\)
\(x^7\times x^5=3^{12}\)
\(x^{12}=3^{12}\)
\(x=3\)
^^
\(\left(x+1\right)^4=\frac{5^8}{25^4}\)
\(\left(x+1\right)^4=\frac{\left(5^2\right)^4}{\left(5^2\right)^4}\)
\(\left(x+1\right)^4=1\)
\(\left[\begin{array}{nghiempt}x+4=1\\x+4=-1\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=1-4\\x=-1-4\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=-3\\x=-5\end{array}\right.\)
^^
\(x^6=x\)
\(\left[\begin{array}{nghiempt}x=1\\x=-1\\x=0\end{array}\right.\)
^^
\(\frac{4^{20}+4^{15}}{4^{10}+4^5}=\frac{4^{15}\times\left(4^5+1\right)}{4^5\times\left(4^5+1\right)}=4^{10}\)
^^
\(A=2^0+2^1+2^2+...+2^{2016}\)
\(2A=2^1+2^2+2^3+...+2^{2017}\)
\(2A-A=\left(2^1+2^2+2^3+...+2^{2017}\right)-\left(2^0+2^1+2^2+...+2^{2016}\right)\)
\(A=2^{2017}-1\)
