Bài 1: a) Viết tích sau dưới dạng một lũy thừa: \(x.x^2.x^3.x^4.x^5.....x^{49}.x^{50}\)
b) So sánh \(4^{15}và8^{11}\)
Bài 2: Tìm x:
\(\left(x-1\right)^4:3^2=3^6\)
Bài 3: So sánh mà không tính giá trị cụ thể :
\(27^{15}va81^{11}\)
Bài 4: Tìm STN n biết rằng :
a) \(256< 2^n< 1024\)
b)\(27< 3^n< 243\)
c)\(16< 4^n< 256\)
d) \(125< 5^n< 3125\)
Bài 1:
\(\text{a) }x.x^2.x^3.x^4.x^5.....x^{49}.x^{50}\)
\(=x^{1+2+3+4+5+...+49+50}\)
\(=x^{\frac{51.50}{2}}\)
\(=x^{1275}\)
\(\text{b) Ta có:}\)
\(4^{15}=\left(2^2\right)^{15}=2^{2.15}=2^{30}\)
\(8^{11}=\left(2^3\right)^{11}=2^{3.11}=2^{33}\)
\(\text{Vì }2^{30}< 2^{33}\text{ nên }4^{15}< 8^{11}\)
Bài 2: Tìm x
\(\left(x-1\right)^4:3^2=3^6\)
\(\Rightarrow\left(x-1\right)^4=3^6\times3^2\)
\(\Rightarrow\left(x-1\right)^4=3^8\)
\(\Rightarrow\left(x-1\right)^4=3^{2.4}\)
\(\Rightarrow\left(x-1\right)^4=\left(3^2\right)^4\)
\(\Rightarrow x-1=9\)
\(\Rightarrow x=10\)
Bài 3 và bài 4 mk làm sau
Bài 1 : a) \(x.x^2.x^3.x^4.....x^{49}.x^{50}=x^{1+2+3+...+49+50}\) (Dễ rồi tự tính)
b) \(\hept{\begin{cases}4^{15}=\left(2^2\right)^{15}=2^{30}\\8^{11}=\left(2^3\right)^{11}=2^{33}\end{cases}}\)Rồi tự so sánh đi
Bài 2 :
\(\left(x-1\right)^4\div3^2=3^6\Leftrightarrow\left(x-1\right)^4=3^8=\left(3^2\right)^4=9^4\Leftrightarrow x-1=9\Leftrightarrow x=10\)
Bài 3 :
\(\hept{\begin{cases}27^{15}=\left(3^3\right)^{15}=3^{45}\\81^{11}=\left(3^4\right)^{11}=3^{44}\end{cases}}\) nt
Bài 4 :
a) \(256< 2^n< 1024\Leftrightarrow2^8< 2^n< 2^{10}\Leftrightarrow n=9\)
b) \(27< 3^n< 243\Leftrightarrow3^3< 3^n< 3^5\Leftrightarrow n=4\)
c) \(16< 4^n< 256\Leftrightarrow4^2< 4^n< 4^4\Leftrightarrow n=3\)
d) \(125< 5^n< 3125\Leftrightarrow5^3< 5^n< 5^5\Leftrightarrow n=4\)
Bài 3 :
Ta có : \(27^{15}=\left[3^3\right]^{15}=3^{45}\)
\(81^{11}=\left[3^4\right]^{11}=3^{44}\)
Mà 45 > 44 => \(3^{45}>3^{44}\)hay \(27^{15}>81^{11}\)
Bài 4 : \(a,256< 2^n< 1024\)
\(\Leftrightarrow2^8< 2^n< 2^{10}\)
\(\Leftrightarrow8< n< 10\Leftrightarrow n=9\)
\(b,27< 3^n< 243\)
\(\Leftrightarrow3^3< 3^n< 3^5\Leftrightarrow3< n< 5\Leftrightarrow n=4\)
\(c,16< 4^n< 256\Leftrightarrow4^2< 4^n< 4^4\Leftrightarrow2< n< 4\Leftrightarrow n=3\)
\(d,125< 5^n< 3125\Leftrightarrow5^3< 5^n< 5^5\Leftrightarrow3< n< 5\Leftrightarrow n=4\)
\(\text{Bài 3: Ta có:}\)
\(27^{15}=\left(3^3\right)^{15}=3^{3.15}=3^{45}\)
\(81^{11}=\left(3^4\right)^{11}=3^{4.11}=3^{44}\)
\(\text{Vì }3^{45}>3^{44}\text{ nên }27^{15}>81^{11}\)
\(\text{Bài 4:}\)
\(\text{a) }256< 2^n< 1024\)
\(\Rightarrow2^8< 2^n< 2^{10}\)
\(\Rightarrow8< n< 10\)
\(\Rightarrow n=9\)
\(\text{b) }27< 3^n< 243\)
\(\Rightarrow3^3< 3^n< 3^5\)
\(\Rightarrow3< n< 5\)
\(\Rightarrow n=4\)
\(\text{c) }16< 4^n< 256\)
\(\Rightarrow4^2< 4^n< 4^4\)
\(\Rightarrow2< n< 4\)
\(\Rightarrow n=3\)
\(\text{d) }125< 5^n< 3125\)
\(\Rightarrow5^3< 5^n< 5^5\)
\(\Rightarrow3< n< 5\)
\(\Rightarrow n=4\)
