Question

If 52x-1 - 25x-1 = 2500 find the value of x

Answer 1

 

Simplify 52x−1−25x−152x-1-25x-152x−1−25x−1 to 27x−1−127x-1-127x−1−1

27x−1−1=250027x-1-1=250027x−1−1=2500


2

 

Simplify 27x−1−127x-1-127x−1−1 to 27x−227x-227x−2

27x−2=250027x-2=250027x−2=2500


3

 

Add 222 to both sides

27x=2500+227x=2500+227x=2500+2


4

 

Simplify 2500+22500+22500+2 to 250225022502

27x=250227x=250227x=2502


5

 

Divide both sides by 272727

x=250227x=\frac{2502}{27}x=​27​​2502​​


6

 

Simplify 250227\frac{2502}{27}​27​​2502​​ to 2783\frac{278}{3}​3​​278​​

x=2783x=\frac{278}{3}x=​3​​278​​


Done

Answer 2

52x-25x-1-1=2500

27x-2=2500
27x=2500+2
27x =2502

x=2502/27
x =(9*278)/9*3

x=278/3