Question

Câu 1 : Tìm x

a, 5^x = 125 

b, 3^2x = 81

c, 5^{2x - 3} - 2.5^{2 =} 5² . 3

Answer 1

a) 5^x = 125

\(\Rightarrow\)5^x = 5³

\(\Rightarrow\)x = 3

b, 3^2x = 81

\(\Rightarrow\)3^2x = 3⁴

\(\Rightarrow\)2x = 4

\(\Rightarrow\)  x = 4 : 2

\(\Rightarrow\)  x = 2

c, 5^2x-3 - 2 . 5² = 5² . 3

5^2x-3 - 2 . 25 = 25 . 3

5^2x-3 - 50 = 75

5^2x-3 = 75 + 50

5^2x-3 = 125

5^2x-3 = 5³

2x - 3 = 3

2x = 3 + 3

2x = 6

  x = 6 : 2

  x = 3

Answer 2

a, 5^x = 125 suy ra 5^x = 5³ suy ra x = 3

b, 3^2x = 81 suy ra 3^2x = 3⁴ suy ra x = 2

c, 5^{2x - 3} - 2.5² = 5² . 3

suy ra 5^2x : 5³ = 5² .3 + 2. 5²

suy ra 5^2x : 5³ = 5² . 5

suy ra 5^2x = 5³ . 5² . 5³

5^2x = 5⁶ suy ra 2x = 6 suy ra x = 3

Answer 3

a) \(5^x\)= 125

\(\Leftrightarrow\)\(5^x\)= \(5^3\)\(\Rightarrow\)x = 3

b) \(3^{2x}\)= 81 

\(\Leftrightarrow\)\(3^{2x}\)= \(3^4\)\(\Rightarrow\)\(2\)x = \(4\) \(\Rightarrow\)x = \(\frac{4}{2}\)= \(2\)

c) \(5^{2x-3}\)- \(2\) . \(5^2\)= \(5^2\). \(3\)

\(\Rightarrow\)\(5^{2x}\): \(5^3\)- \(2\) . \(5^2\)= \(5^2\). \(3\)

\(\Rightarrow\)\(5^{2x}\): \(5^3\)= \(5^2\). \(3\) + \(5^2\). \(2\)

\(\Rightarrow\)\(5^{2x}\): \(5^3\)= \(5^2\). \(\left(3+2\right)\)

\(\Rightarrow\)\(5^{2x}\): \(5^3\)= \(5^2\). \(5\)= \(5^3\)

\(\Rightarrow\)\(5^{2x}\)= \(5^3\). \(5^3\)= \(5^6\)

\(\Rightarrow\)\(2x\)= \(6\)

\(\Rightarrow\)\(x\)= \(\frac{6}{2}\)= \(3\)