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6)\(3.\left(x+1\right)-2^3.2=11\)
\(3\left(x+1\right)-2^4=11\)
\(3.\left(x+1\right)=11+16\)
3.(x+1)=27
x+1=27:3
x+1=9
x=9-1
x=8
Vậy x=8
7) \(180-2.\left(x+5\right)^2=130\)
\(2.\left(x+5\right)^2=180-130\)
2.(x+5)2=50
(x+5)2=50:2
(x+5)2=25
x+5=5 hoặc x+5=-5
x=5-5 x=-5-5
x=0 x=-10
Vậy x=0 hoặc x=-10
Bài 1:
\(2B=2^2+2^3+2^4+2^5+...+2^{101}\\ \Rightarrow2B-B=2^{101}-2\\ \Leftrightarrow B=2^{101}-2\)
\(3C=3+3^2+3^3+3^4+...+3^{2004}\\ \Rightarrow3C-C=3^{2004}-3\\ \Leftrightarrow2C=3^{2004}-3\\ \Leftrightarrow C=\frac{3^{2004}-3}{2}\)
Mấy câu sau tương tự nhân 4 và 5 nhé bạn!
Bài 2: Giải theo lớp 6 nhé! :) Mình nghĩ đề bài cần a nguyên nữa nhé nếu không giải theo lớp 8,9 mất rồi! :)
\(a,2a+27⋮2a+1\\ \Leftrightarrow2a+1+26⋮2a+1\\ \Rightarrow26⋮2a+1\left(vì2a+1⋮2a+1\right)\\ \Rightarrow2a+1\inƯ_{\left(26\right)}mà2a+1lẻnên:\\ 2a+1\in\left\{1;-1;13;-13\right\}\\ \Leftrightarrow a\in\left\{0;-1;6;-7\right\}\\ Vậy...\)
Mấy bài sau tương tự nhé! :)
\(2^x=2\Rightarrow x=1\)
\(2^{2x+2}=8^2\Rightarrow2^{2x+2}=2^6\Rightarrow2x+2=6\)\(2x=6-2=3\Rightarrow x=3:2=\frac{3}{2}\)
2. A = 3 + 32 + 33 +...+ 3100
=> 3A = 32 + 33 +...+ 3101
=> 3A - A = 3101 -3
=>2A = 3101 - 3
=>2A + 3 =3101 - 3 + 3=3101
Vậy 2A+3 là 1 lũy thừa của 3
1.
a) 2711 và 818
2711 = (33)11 = 333
818 = (34)8 = 332
\(\Rightarrow\) 2711 > 818
A= 82 . 324 = (23)2 . (25)4 = 26.220 = 226
\(B=27^3.9^4.81^2\)
\(=\left(3^3\right)^3.\left(3^2\right)^4.\left(3^4\right)^2\)
\(=3^9.3^8.3^8\)
\(=3^{25}\)
A) \(2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(3^{200}=\left(3^2\right)^{100}=9^{100}\)
do \(8^{100}< 9^{100}=>A< B\)
B) \(27^5=\left(3^3\right)^5=3^{15}\)
\(243^3=\left(3^5\right)^3=3^{15}\)
=> \(27^5=243^3\)
c/ 2x - 1 = \(5^{98}:5^{96}\)
2x - 1 = \(5^2\) = 25
2x = 25 + 1 = 26
x = 26 : 2
x = 13
d/ 7x + 3 = \(3^5.2^3.9\)
7x + 3 = \(3^5.3^2.8=3^7.8=2187.8\)
7x + 3 = \(17496\)
7x = 17496 - 3 = 17493
x = 17493 : 7
x = 2499
e/\(2^{2x+6}=1\)
\(2^{2x+6}=2^0\)
2x + 6 = 0
2x = 0 - 6 = - 6
x = - 6 : 2
x = - 3
j/ \(2^x=8\)
\(2^x=2^3\)
x = 3
g/ \(2^x:2^3=16\)
\(2^{x-3}=2^4\)
x - 3 = 4
x = 4 + 3
x = 7
h/ \(2^x+2^{x+1}+2^{x+2}=56\)
\(2^x\left(1+2+2^2\right)\) = 56
\(2^x.7=56\)
\(2^x=56:7\)
\(2^x=8\)
\(2^x=2^3\)
x = 3
Bài a, b thiên phong giải r, mk chỉ làm những bài còn lại thôi. Chúc bạn học tốt!!!
\(5.2^2-27:3^2\)
\(=5.4-27:9\)
\(=20-3=17\)
TL
=5.4-27:9
=20-3
=17
Hok tốt