Question

25^n-1+100=5^(2n-1) please solve this questions quickly​

Answer 1

Step-by-step explanation:

Given:-

25^n-1+100=5^(2n-1)

To find:-

Find the value of n ?

Solution:-

Given equation is 25^n-1+100=5^(2n-1)

It can be written as (5^2)^(n-1) +100 = 5^(2n-1)

We know that

(a^m)^n = a^(mn)

=>5^2(n-1) +100 = 5^(2n-1)

=>5^(2n-2) +100 = 5^(2n-1)

We know that a^m/a^n =a^(m-n)

=>(5^2n /5^2 )+100 = 5^2n/5^1

=>(5^2n /25) + 100 = 5^2n /5

=>(5^2n /25) -(5^2n /5) = -100

=>5^2n [(1/25)-(1/5)]= -100

=>5^2n[ (1-5)/25] = -100

=>5^2n (-4/25) = -100

=>5^2n = -100×(25/-4)

=>5^2n =100×25/4

=>5^2n = 25×25

=>5^2n = 625

=>5^2n = 5^4

On comparing both sides then

=>2n = 4

=>n = 4/2

=>n = 2

Answer:-

The value of n for the given problem is 2

Check:-

If n=2 then

LHS:-

25^n-1+100

=>25^(2-1)+100

=>25+100

=>125

RHS:-

5^(2n-1)

=>5^(2×2-1)

=>5^(4-1)

=>5^3

=>5×5×5

=>125

LHS = RHS is true for n =2

Used formulae:-

• (a^m)^n = a^(mn)
• a^m/a^n =a^(m-n)