Interestin Math Question from Olympiad -1

 Interesting Math Question from Olympiad-1 

In this blog we are going to solve this Question

`\left( \frac{5^{x}+25^{x}}{5^{x}} \right) = 26`

I can Write `25^{x} as 5^{x}\times5^{x}` , we get

` \left( \frac{5^{x}+(5^{x}\times 5^{x}) }{5^{x}} \right) = 26`

Take `5^{x}` common from numerator , we get

` \left( \frac{5^{x}+(1+ 5^{x}) }{5^{x}} \right) = 26`

cancelling `5^{x}` in numerator and denominator we will get

`(1+5^{x}) = 26`
`5^{x} = 26-1`

`5^{x}=25`
`5^{x}=5^{2}`
Equating raise to the power we will get
x= 2 that is our answer