Question

If 5^2x-1 - (25)^x-1 = 2500, then find the value of x.

Answer 1

Given Equation is 5^2x - 1 - (25)^x - 1 = 2500.

$5^{2x-1} - (5^{2)^{x-1} } = 2500$

$5^{2x-1} - 5^{2(x-1)} = 2500$

$5^{2x} * 5^{-1} - 5^{2x} * 5^{-2} = 2500$

$5^{2x}( 5^{-1} - 5^{-2}) = 2500$

$5^{2x} = \frac{2500}{ 5^{-1} - 5^{-2} }$

$5^{2x} = \frac{2500}{ \frac{4}{25} }$

$5^{2x} = \frac{2500 * 25}{4}$

$5^{2x} = 15625$

$5^{2x} = 5^6$

$2x = 6$

$x = 3$



Hope this helps!   --------------- Good Luck

Answer 2

2x−1​​−(5​2)​x−1​​​​=2500 





5^{2x-1} - 5^{2(x-1)}




= 25005​2x−1​​−5​2(x−1)​​=2500 




5^{2x} * 5^{-1} - 5^{2x} * 5^{-2}





= 25005​2x​​∗5​−1​​−5​2x​​∗5​−2​​=2500 





5^{2x}( 5^{-1} - 5^{-2})




= 25005​2x​​(5​−1​​−2)=2500 

5^{2x}



= { 2500}{ 5^{-1} - 5^{-2




5​2x​​=​5​−1​​−5​−2​​​​2500​​ 

5^{2x} = {2500}




4 * 25} }5​2x​​=



​​25​​4​​​​2500​​ 

5^{2x} =


{2500 * 25}{4}5​2x​​=​4​​2500∗25​​ 







5^{2x}



= 156255​2x​​=15625 

5^{2x}

= 5^65​2x​​=5​6​​ 

2x

= 62x=6 




x = 3x=3 




****** 3x =.3