Question

If 25n-1 + 100= 5²n-1, then the value of n is​

Answer 1

Answer:

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

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

100= 5^(2n-1) - (5)^2*(n-1)

[Use Formula: {(a)^n}^m=a^nm ]

100= 5^(2n-1) - (5)^2*(n-1)

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

100= 5^(2n-1) (1–5^-1)

100= 5^(2n-1) (1–1/5)

100 = 5^(2n-1) (4/5)

100*5/4. =5^(2n-1)

125= 5^(2n-1)

5^3=5^(2n-1)

{Use Formula

If a^m=a^n Then m=n}

3=2n-1

3+1=2n

2n=4

n=4/2

n=2

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

25^n.25^-1 + 100= 5^2n.5^-1

25^n.25^-1 + 100= 25^n.5^-1

Now take 25^n.25^-1 part to RHS then will get

25^n.5^-1 - (25^n.25^-1 )=100

Now take 25^n common from LHS

25^n(1/5 - 1/25)= 100

25^n(4/25)=100

25^n=100*25/4

25^n=25*25

25^n=25^2

Now we can say that

n=2.

I hope this helps

Answer 2

Answer:

n is equal to 2

Step-by-step explanation

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