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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, \(\left(x-5\right)^{2018}=9.\left(x-5\right)^{2016}\)
\(\Rightarrow\dfrac{\left(x-5\right)^{2018}}{\left(x-5\right)^{2016}}=9.\dfrac{\left(x-5\right)^{2016}}{\left(x-5\right)^{2016}}\)
\(\Rightarrow\left(x-5\right)^2=9\)
\(\Leftrightarrow\left(x-5\right)^2=3^2\)
\(\Rightarrow x-5=3\)
\(\Rightarrow x=3+5\)
\(\Rightarrow x=8\)
\(\Leftrightarrow\dfrac{7^x\left(7^2+7+1\right)}{57}=\dfrac{5^{2x}\left(1+5+125\right)}{131}\)
=>7^x=5^2x
=>x=0
a: \(\Leftrightarrow2x+7=-4\)
=>2x=-11
hay x=-11/2
b: \(\Leftrightarrow\dfrac{7^x\cdot49+7^x\cdot7+7^x}{57}=\dfrac{5^{2x}+5^{2x+1}+5^{2x+3}}{131}\)
\(\Leftrightarrow7^x=5^{2x}\)
=>x=0
1 / 5 x 2 2 + ( x + 3 ) = 5 2
20 + ( x + 3 ) = 25
x + 3 = 5
x = 2
2 / 3 2 x 2 + ( x + 25 ) = 10 2
18 + ( x + 25 ) = 100
x + 25 = 82
x = 57
3 / 2 3 x 5 - ( x + 3 2 ) = 10
40 - ( x + 9 ) = 10
x + 9 = 30
x = 21
4 / 7 2 - 7 x ( 13 - x ) = 14
49 - 7 x ( 13 - x ) = 14
7 x ( 13 - x ) = 35
13 - x = 5
x = 8
5 / 14 x - 2 x 7 2 = 2 x 3 x 7
14 x - 98 = 42
14 x = 140
x = 10
1/ 5 x 22 + ( x + 3 ) = 52
2/ 32 x 2 + ( x + 25 ) = 102
3/ 23 x 5 - ( x + 32 ) = 10
4/ 72 - 7 x ( 13 - x ) = 14
5/ 14x - 2 x 72 = 2 x 3 x 7
1 / 5 x 2 2 + ( x + 3 ) = 5 2
20 + ( x + 3 ) = 25
x + 3 = 5
x = 2
2 / 3 2 x 2 + ( x + 25 ) = 10 2
18 + ( x + 25 ) = 100
x + 25 = 82
x = 57
3 / 2 3 x 5 - ( x + 3 2 ) = 10
40 - ( x + 9 ) = 10
x + 9 = 30
x = 21
4 / 7 2 - 7 x ( 13 - x ) = 14
49 - 7 x ( 13 - x ) = 14
7 x ( 13 - x ) = 35
13 - x = 5
x = 8
5 / 14 x - 2 x 7 2 = 2 x 3 x 7
14 x - 98 = 42
14 x = 140
x = 10
nhé !
\(7^x+7^{x+1}+7^{x+2}=3\cdot19\cdot343\)
\(\Leftrightarrow7^x=343\)
hay x=3
có thể giải thích rõ hơn đc ko ạ xin cảm ơn