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(7x-11mũ 3)=2.2.2.2.2.5mũ 90
2.2.2.2.2.5mũ 90 =14400
7x=74
(7x - 11)3 = 25.52 + 200
=> (7x - 11)3 = 800 + 200
=> (7x - 11)3 = 1000
=> (7x - 11)3 = 103
=> 7x - 11 = 10
=> 7x = 10 + 11
=> 7x = 21
=> x = 21 : 7 = 3
3x + 25 = 26.22 + 2.30
=> 3x + 25 = 104 + 2
=> 3x + 25 = 106
=> 3x = 106 - 25
=> 3x = 81
=> 3x = 34
=> x = 4
a)\(\left(7x-11\right)^3=2^5.5^2+200\) b) \(3^x+25=26.2^2+2.3^0\)
\(\left(7x-11\right)^3=32.25+200\) \(3^x+25=26.4+2.1\)
\(\left(7x-11\right)^3=800+200\) \(3^x+25=104+2\)
\(\left(7x-11\right)^3=1000\) \(3^x+25=106\)
\(\Rightarrow\left(7x-11\right)^3=10^3\) \(3^x=106-25\)
\(\Rightarrow7x-11=10\) \(3^x=81\)
\(7x=10+11\) \(3^x=3^4\)
\(x=\frac{21}{7}\) \(\Rightarrow x=4\)
\(x=3\) Vậy x = 4
Vậy x = 3
\(\left(7x-11\right)^3=25.5^2+200\)
\(\left(7x-11\right)^3=25.25+200\)
\(\left(7x-11\right)^3=625+200\)
\(\left(7x-11\right)^3=825\)
Hình như đề sai rồi bạn ơi
Giải:
\(a,2^x-15=17.\)
\(2^x=17+15.\)
\(2^x=32.\)
\(2^x=2^5.\)
\(\Rightarrow x=5\in N.\)
Vậy \(x=5.\)
\(b,\left(7x-11\right)^3=2^5.5^2+200.\)
\(\left(7x-11\right)^3=32.25+200.\)
\(\left(7x-11\right)^3=800+200.\)
\(\left(7x-11\right)^3=1000.\)
\(\left(7x-11\right)^3=10^3.\)
\(\Rightarrow7x-11=10.\)
\(\Rightarrow7x=10+11=21.\)
\(\Rightarrow x=21:7=3\in N.\)
Vậy \(x=3.\)
\(c,3^x+25=26.2^2+2.3^0.\)
\(3^x+25=26.2^2+2.1.\)
\(3^x+25=2\left(26.2+1\right).\)
\(3^x+25=2.53.\)
\(3^x+25=106.\)
\(3^x=106-25.\)
\(3^x=81.\)
\(3^x=3^4\Rightarrow x=4\in N.\)
Vậy \(x=4.\)
\(d,49.7^x=2041.\)(đề này sai).
Sửa đề:
\(49.7^x=2401.\)
\(7^x=2401:49.\)
\(7^x=49.\)
\(7^x=7^2\Rightarrow x=2\in N.\)
Vậy \(x=2.\)
\(e,3^x=243.\)
\(3^x=3^5\Rightarrow x=5\in N.\)
Vậy \(x=5.\)
~ Học tốt!!! ~
a, \(2^x-15=17\)
\(\Rightarrow2^x=32\Rightarrow2^x=2^5\)
Vì \(2\ne-1;2\ne0;2\ne1\) nên \(x=5\)
Vậy....
b, \(\left(7x-11\right)^3=2^5.5^2+200\)
\(\Rightarrow\left(7x-11\right)^3=32.25+200\)
\(\Rightarrow\left(7x-11\right)^3=1000=10^3\)
\(\Rightarrow7x-11=10\Rightarrow7x=21\Rightarrow x=3\)
Vậy.....
c, \(3^x+25=26.2^2+2.3^0\)
\(\Rightarrow3^x+25=26.4+2\)
\(\Rightarrow3^x=104+2-25\)
\(\Rightarrow3^x=81=3^4\)
Vì \(3\ne-1;3\ne0;3\ne1\) nên x=4
Vậy.....
d,Sửa đề:\(49.7^x=2401\)
\(\Rightarrow7^2.7^x=7^4\Rightarrow7^{2+x}=7^4\)
Vì \(7\ne-1;7\ne0;7\ne1\) nên \(2+x=4\Rightarrow x=2\)
Vậy.....
Câu e làm tương tự! Chúc bạn học tốt!!!
\(a,\left(7x-11\right)^3=2^5.5^2+200.\)
\(\left(7x+11\right)^3=32.25+200.\)
\(\left(7x+11\right)^3=800+200.\)
\(\left(7x-11\right)^3=1000.\)
\(\left(7x-11\right)^3=10^3.\)
\(\Rightarrow7x-11=10.\)
\(\Rightarrow x=\left(10+11\right):3=7\in Z.\)
Vậy.....
\(b,3^x+25=26.2^2+2.3^0.\)
\(3^x+25=26.4+2.\)
\(3^x+25=104+2.\)
\(3^x+25=106.\)
\(3^x=106-25.\)
\(3^x=81.\)
\(3^x=3^4\Rightarrow x=4\in Z.\)
Vậy.....
\(c,2^x+3.2=64.\)(có vấn đề).
\(d,5^{x+1}+5^x=750.\)
\(5^x.5^1+5^x+1=750.\)
\(5^x\left(5^1+1\right)=750.\)
\(5^x\left(5+1\right)=750.\)
\(5^x.6=750.\)
\(5^x=750:6.\)
\(5^x=125.\)
\(5^x=5^3\Rightarrow x=3\in Z.\)
Vậy.....
\(e,x^{15}=x.\)
\(\Rightarrow x\left(x^{14}-1\right)=0\Rightarrow\left\{{}\begin{matrix}x=0\\x=1\end{matrix}\right..\)
\(f,\left(x-5\right)^4=\left(x-5\right)^6.\)
\(\Leftrightarrow\left(x-5\right)^4-\left(x-5^6\right)=0.\)
\(\Leftrightarrow\left(x-5\right)^4\left[1-\left(x-5\right)^2\right]=0.\)
\(\Leftrightarrow\left(x-5\right)^4\left(1-x+5\right)\left(1+x-5\right)=0.\)
\(\Leftrightarrow\left(x-5\right)^4\left(6-x\right)\left(x-4\right)=0.\)
\(\Leftrightarrow\left(x-5\right)^4=0\Rightarrow x-5=0\Rightarrow x=5\in Z.\)
\(6-x=0\Rightarrow x=6\in Z.\)
\(x-4=0\Rightarrow x=4\in Z.\)
Vậy.....
d. 2x+2 - 2x = 96 e. (7x-11)3 = 25 . 52
=> 2x.22 - 2x = 96 => (7x-11)3 = 1000 = 103
=> 2x(22 - 1) = 96 => 7x - 11 = 10
=> 2x.3 = 25.3 => 7x = 21
=> x = 5 => x = 3
Câu e đề sai nhé! Mỏi tay ...
d.\(2^{x+2}-2^x=96\)
\(2^x\left(2^2-1\right)=96\)
\(2^x.3=96\)
\(2^x=32=2^5\)
\(\Rightarrow x=5\)
Vậy.......
e)Đề sai hả bạn ?
a) 135 - 5(x + 4) = 35
<=> 135 - 5x - 20 = 35
<=> 115 - 5x = 35
<=> 5x = 115 - 35
<=> 5x = 80
<=> x = 16
b) 25 + 3 (x - 8) = 106
=> 3 ( x - 8) = 106 - 25
=> 3 ( x - 8) = 81
=> ( x - 8) = 81: 3
=> x - 8 = 27
=> x = 27 + 8
=> x = .......