2^x nhân 2^x ^+^4 = 256
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SM
7 tháng 8 2018
a) 4x . 42 = 256
=> 4x . 16 = 256
=> 4x = 256 : 16
=> 4x = 16
=> 4x = 42
=> x = 2
b) x5 = 243
=> x5 = 35
=> x = 5
20 tháng 6 2015
a.\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2015}\right)=\frac{1}{2}.\frac{2}{3}...\frac{2014}{2015}=\frac{1.2.3...2014}{2.3...2015}=\frac{1}{2015}\)
b.\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{128}-\frac{1}{256}=1-\frac{1}{256}=\frac{255}{256}\)
c.\(\frac{5}{2}+\frac{5}{4}+\frac{5}{8}+...+\frac{5}{256}=5\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\right)=5.\frac{255}{256}=\frac{1275}{256}\)
d.14,35+(13,7-13,6).1=14,35+0,1.1=14,35+0,1=14,45
17 tháng 12 2017
=> 2^x.(17-2^4) = 256
=> 2^x.1= 256
=> 2^x = 256 = 2^8
=> x=8
k mk nha
IM
25 tháng 8 2016
Đặt bểu thức là A
Ta có :
\(A=2^0.2^1.2^2.....2^8\)
\(\Rightarrow A=2^{0+1+2+3+...+8}\)
\(\Rightarrow A=2^{36}\)
25 tháng 8 2016
1x2x4x8x16x...x256=20x21x22x23x...x28
=20+1+2+3+4+...+8
=236
vậy 1x2x4x8x..x256=236
HT
0
ND
Nguyễn Đức Trí
VIP
11 tháng 7 2023
a) \(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{8}+...-\dfrac{1}{128}+\dfrac{1}{128}-\dfrac{1}{256}\)
\(=1-\dfrac{1}{256}\)
\(=\dfrac{255}{256}\)
b) \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{13.14}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{14}\)
\(=1-\dfrac{1}{14}\)
\(=\dfrac{13}{14}\)
c) \(\dfrac{3}{15.18}+\dfrac{3}{18.21}+\dfrac{3}{21.24}+...+\dfrac{3}{87.90}\)
\(=3.\left(\dfrac{1}{15.18}+\dfrac{1}{18.21}+\dfrac{1}{21.24}+...+\dfrac{1}{87.90}\right)\)
\(=3.\left[\dfrac{1}{3}.\left(\dfrac{1}{15}-\dfrac{1}{18}\right)+\dfrac{1}{3}.\left(\dfrac{1}{18}-\dfrac{1}{21}\right)+\dfrac{1}{3}.\left(\dfrac{1}{21}-\dfrac{1}{24}\right)+...+\dfrac{1}{3}.\left(\dfrac{1}{87}-\dfrac{1}{90}\right)\right]\)
\(=3.\dfrac{1}{3}.\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)
\(=\dfrac{1}{15}-\dfrac{1}{90}\)
\(=\dfrac{6}{90}-\dfrac{1}{90}\)
\(=\dfrac{5}{90}=\dfrac{1}{18}\)
11 tháng 12 2022
Đặt x/1=y/2=k
=>x=k; y=2k
x^4*y^4=256
=>k^4*16k^4=256
=>16k^8=256
=>k^8=16
=>k^4=4
=>k^2=2
TH1: \(k=\sqrt{2}\)
=>\(x=\sqrt{2};y=2\sqrt{2}\)
TH2: \(k=-\sqrt{2}\)
=>\(x=-\sqrt{2};y=-2\sqrt{2}\)
\(2^x.2^{x+4+}=256\\ 2^{x+x+4}=256\\ 2^{2x+4}=256\\ 2^{2x+4}=2^8\\ \Rightarrow 2x+4=8\\ \Rightarrow2x=8-4\\ \Rightarrow2x=4\\ \Rightarrow x=\dfrac{4}{2}=2\)
=>2^(x+x+4)=2^8
=>2x+4=8
=>2x=4
=>x=2