Question

Tìm số tự nhiên x , biết:

1) 49 . 7\(^x\) = 2401

2) 25 : 5\(^x\) = 5\(^x\)

Answer 1

49 . 7^x = 2401

=> 7² . 7^x = 7⁴

7^x = 7⁴ : 7²

7^x = 7²

=> x = 2

2) 25 : 5^x = 5^x

VD : 5^x : 5^x = 1

=> 25 : 5 = 5

=> 25 : 5¹ = 5¹

=> x = 1

Answer 2

1) 49 . 7^x = 2401

7^x = 2401 : 49

7^x = 49

=> 7^x = 7²

=> x = 2

Vậy x = 2

2) 25 : 5^x = 5^x

=> 5² = 5^x . 5^x

=> 5² = 5^{x + x}

=> 2 = x + x

=> 2 = 2x

=> x = 2 : 2

=> x = 1

Vậy x = 1

Chúc bạn học tốt!

Answer 3

\(a\))\(49.7^x\)\(=2401\)

\(\Rightarrow\) \(7^x\)\(=2401\div49\)

\(\Rightarrow\)\(7^x\) \(=49\)

\(\Leftrightarrow\) \(7^x\)\(=7^2\)

\(\Rightarrow\) \(x=2\)

\(b\)) \(25\div5^x\) \(=5^x\)

\(\Leftrightarrow5^2\) \(\div5^x\) \(=5^x\)

\(\Rightarrow\) \(5^2\) \(=5^x\)\(.5^x\)

\(\Rightarrow\) \(2=x+x\)

\(\Leftrightarrow\) \(2=2x\)

\(\Rightarrow\) \(x=2\div2\)

\(\Rightarrow\) \(x=1\)