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\(7.7^{x+1}=343\)
\(\Rightarrow7.7^{x+1}=7^3\)
\(\Rightarrow7^{x+1}=7^3:7\)
\(\Rightarrow7^{x+1}=7^2\)
\(\Rightarrow x+1=2\)
\(\Rightarrow x=2-1=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(5^x\cdot5^{x-1}=125\)
\(5^{x+x-1}=5^3\)
\(5^{2x-1}=5^3\)
\(\Rightarrow2x-1=3\)
\(\Rightarrow x=2\)
\(343:7^x=7\)
\(343=7^{x+1}\)
\(7^3=7^{x+1}\)
\(\Rightarrow x+1=3\)
\(\Rightarrow x=2\)
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Bai 1
75:73-343:7
=49-49=0
Bai 2
a. 3x:32=243
=> 3x-2=243
=> x-2=5
=> x=7(bạn viết sai đề câu này phải là 243)
b. x=-1;0;1
c. 2x.64=26
=> 2x.26=26
=> 2x=1
=> x=0
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\(\left(\frac{3}{7}\right)^5.\left(\frac{7}{3}\right)^{-1}.\left(\frac{5}{6}\right)^6.\left(\frac{343}{625}\right)^{-2}\)
\(=\left(\frac{3}{7}\right)^5.\left(\frac{3}{7}\right).\left(\frac{5}{2.3}\right)^6.\left(\frac{5^4}{7^3}\right)^2\)
\(=\frac{3^5}{7^5}.\frac{3}{7}.\frac{5^6}{2^6.3^6}.\frac{5^8}{7^6}=\frac{1}{2^6}.\frac{3^6}{3^6}.\frac{5^{14}}{1}.\frac{1}{7^{12}}=\frac{5^{14}}{2^6.7^{12}}\)
Nó đâu có phải là số nguyên đâu
3/7 x 5/6 +5/6 x3/7
= (3/7x5/6) + (5/6x3/7)
= 15/42 + 15/42 = 30/42 = 5/7
![](https://rs.olm.vn/images/avt/0.png?1311)
a)\(\dfrac{1}{3}^x=\dfrac{1}{729}\)
\(\dfrac{1}{3}^x=\dfrac{1}{3}^6\)
Suy ra x=6
vậy x=6
b)\(\left(\dfrac{1}{3}-\dfrac{1}{2}\right)^x=\dfrac{1}{36}\)
\(\left(-\dfrac{1}{6}\right)^x\)=\(\dfrac{1}{6}^2\)
Do đó x=2
Vậy x=2
c)\(\dfrac{25}{5}^x=\dfrac{1}{125}\)
\(5^x=5^{-3}\)
Suy ra x=-3
Vậy x=-3
d)\(7^{2n-\dfrac{1}{49}}=-343\)
\(-7^{2n-\dfrac{1}{49}}=-7^3\)
Do đó \(2n-\dfrac{1}{49}=3\)
2n=\(\dfrac{148}{49}\)
n=\(\dfrac{74}{49}\)
vậy n=\(\dfrac{74}{49}\)
chúc bạn học tốt ạ
![](https://rs.olm.vn/images/avt/0.png?1311)
3x : 3 = 81
=> 3x = 81 . 3 = 243 = 35
=> x = 5
22x : 8 = 128
=> 22x = 128 . 8 = 1024 = 210
=> 2x = 10
=> x = 10 : 2
=> x = 5
7x-1 . 49 = 343
7x-1 = 343 : 49 = 7 = 71
=> x - 1 = 1
=> x = 1+1
=> x = 2
\(7^{x-1}=343\)
\(7^{x-1}=7^3\)
\(\Rightarrow x-1=3\)
\(x=4\)
Vậy ...
7( x - 1 ) = 343
7( x - 1 ) = 73
x - 1 = 3
x = 3 + 1
x = 4