If 25 to the power (n - 1)+100=5 to the power 2n-1 , find the value of n
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Answer:
value of n=2
Step-by-step explanation:
Given,
25^{n-1}+100=5^{2 n-1}25n−1+100=52n−1
On grouping the powered terms we get,
100=5^{2 n-1}-25^{n-1}100=52n−1−25n−1
100=\frac{25^{n}}{5}-\frac{25^{n}}{25}100=525n−2525n
Taking 25^{n}25n as common we get,
100=25^{n} \times \frac{4}{25}100=25n×254
\frac{100 \times 25}{4}=25^{n}25^{2}=25^{n}4100×25=25n252=25n
n=2
So the value of n is 2
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