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a, \(\left(2x+7\right)^4=10^{11}:10^7\)
\(\Rightarrow\left(2x+7\right)^4=10^4\)
\(\Rightarrow2x+7=10\)
\(\Rightarrow2x=10-7\)
\(\Rightarrow2x=3\)
\(\Rightarrow x=\dfrac{3}{2}\) hay \(x=1,5\)
b, \(5^{x-1}.7^{x-1}=25.49\)
\(\Rightarrow\)\(5^{x-1}.7^{x-1}=5^2.7^2\)
\(\Rightarrow\left\{{}\begin{matrix}5^{x-1}=5^2\\7^{x-1}=7^2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x-1=2\\x-1=2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=3\\x=3\end{matrix}\right.\)
c, \(\left(x-5\right)^{2018}=9.\left(x-5\right)^{2016}\)
\(\Rightarrow\dfrac{\left(x-5\right)^{2018}}{\left(x-5\right)^{2016}}=9.\dfrac{\left(x-5\right)^{2016}}{\left(x-5\right)^{2016}}\)
\(\Rightarrow\left(x-5\right)^2=9\)
\(\Leftrightarrow\left(x-5\right)^2=3^2\)
\(\Rightarrow x-5=3\)
\(\Rightarrow x=3+5\)
\(\Rightarrow x=8\)
a. => \(2^{6+x}=2^{10}\)
=> 6+x=10
=> x=10-6
Vậy x=4.
b. => \(7^{3x-1}:7^2=7^6\)
=> 73x-1-2=76
=> 73x-3=76
=> 3x-3=6
=> 3x=6+3
=> 3x=9
Vậy x=3.
c. =>\(7^{5x-1}-25=24\)
=>75x-1=24+25
=>75x-1=49
=>75x-1=72
=>5x-1=2
=>5x=3
Vậy x=\(\frac{3}{5}\).
d. => \(10^{x-3}=10^0\)
=>x-3=0
Vậy x=3.
e. => 2x=10
=> x=10:2
Vậy x=5.
mình thiếu 1 câu hhi
b) {( 10 - 2 . 3 ) .5] + 2 -2 . 6 } : 2 + ( 4 . 5 ) 2
a) (3x-24)73=2.74
3x-24=2.7 (Chia cả hai vế cho 73)
3x-16=14
3x=30
X=10
b)[(10 -x).2+5] : 3 -2 =3
(20-2x+5):3=5
25-2x=15
2x=10
X=5
Bài 2
{[(32+1).10-(8:2+6)]:2}+55-(10:5)3
={(9+1).10-10]:2}+55-23
=[(10.10-10):2]+55-8
=(90:2)+55-8
=45+55-8
=100-8
=92
\(C=1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{18}}=1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{8}+...+\dfrac{1}{131072}-\dfrac{1}{262144}=1+1-\dfrac{1}{262144}=2-\dfrac{1}{262144}\)
a) {[( 32 + 1 ) . 10 - ( 8 : 2 + 6 ) ] : 2 } + 55 -( 10 : 5 )3
= ( 10 . 10 - 10 : 2 ) + 55 - 6
= 90 : 2 ) + 55 - 6
= 45 + 55 - 6
= 100 - 6
= 94
b) 100 - [ 60 - ( 9 - 2 )2 ] . 32
= 100 - [ 60 - 72 ] . 9
= 100 - [ 60 - 49 ] . 9
= 100 - 11 . 9
= 100 - 99
= 1
c) [ ( 1253 ) . 75 - ( 175 )5 : 5 ] : 20162017
= 0 : 20162017
= 0
+ bài d kg hiểu! Xin lỗi
Bài 1:
a: \(7^6+7^5-7^4=7^4\left(7^2+7-1\right)=7^4\cdot55⋮11\)
b: \(10^9+10^8+10^7\)
\(=10^7\left(10^2+10+1\right)=10^7\cdot111⋮111\)
2.
\(\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot15\cdot37\right)\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot5\cdot3\cdot37\right)\\=\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-\left(13\cdot5\right)\cdot\left(3\cdot37\right)\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-65\cdot111\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot0\\ =0\)
\(\Rightarrow10-\left(x-3\right):2=49-1=48\\ \Rightarrow\left(x-3\right):2=-38\\ \Rightarrow x-3=-76\\ \Rightarrow x=-73\)
\(10-\left(x-3\right):2=7^2-1^{10}\)
\(\Rightarrow10-\left(x-3\right):2=48\)
\(\Rightarrow\left(x-3\right):2=-38\)
\(\Rightarrow x-3=-76\Rightarrow x=-73\)