Question

if 25^n-1+100=5^2n-1 find the value of n

Answer 1

Answer:

The value of n=2

Solution:

Given,

$25^{n-1}+100=5^{2 n-1}$

On grouping the powered terms we get,

$100=5^{2 n-1}-25^{n-1}$

$100=\frac{25^{n}}{5}-\frac{25^{n}}{25}$

Taking $25^{n}$ as common we get,

$100=25^{n} \times \frac{4}{25}$

$\frac{100 \times 25}{4}=25^{n}25^{2}=25^{n}$

n=2

So the value of n is 2  

Answer 2

step by step explanation :

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

n−1

+100=5

2n−1

On grouping the powered terms we get,

100=5^{2 n-1}-25^{n-1}100=5

2n−1

−25

n−1

100=\frac{25^{n}}{5}-\frac{25^{n}}{25}100=

5

25

n

−

25

25

n

Taking 25^{n}25

n

as common we get,

100=25^{n} \times \frac{4}{25}100=25

n

×

25

4

\frac{100 \times 25}{4}=25^{n}25^{2}=25^{n}

4

100×25

=25

n

25

2

=25

n

n=2

So the value of n is 2