Question

Tìm \(x,y\) biết :

\(5^{2x-1}=5^{2x-3}+125.24\)

Answer 1

5^{2x - 1} = 5^{2x - 3} + 125 . 24

5^{2x - 1} - 5^{2x - 3} = 125 . 24

5^{2x - 1} . (1 - \(\frac{1}{25}\)) = 3 000

5^{2x - 1} . \(\frac{24}{25}\) = 3 000

5^{2x - 1} = 3 000 : \(\frac{24}{25}\)

5^{2x - 1} = 3 125

5^{2x - 1} = 5⁵

2x - 1 = 5

2x = 5 + 1

2x = 6

x = 6 : 2

x = 3

Answer 2

\(5^{2x-1}=5^{2x-3}+125.24\)

\(5^{2x}:5=5^{2x}:5^3+3000\)

\(5^{2x}:5.5^3=5^{2x}+3000\)

\(5^{2x}.5^2=5^{2x}+3000\)

\(5^{2x}.5^2-5^{2x}.1=3000\)

\(5^{2x}\left(25-1\right)=3000\)

\(5^{2x}=125=5^3\)

=> 2x = 3

=> x = 3/2