Question

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

Answer 1

${25}^{n - 1} + 100 = {5}^{2n - 1} \\ {5}^{2n - 2} + 100 = {5}^{2n - 1} \\ {5}^{2n - 2} - {5}^{2n - 1} = - 100 \\ \frac{ {5}^{2n} }{25} - \frac{ {5}^{2n} }{5} = - 100 \\ {5}^{2n} ( \frac{1}{25} - \frac{1}{5} ) = - 100 \\ {5}^{2n} ( \frac{ - 4}{25} ) = - 100 \\ {5}^{2n} = 25 \times 25 \\ {5}^{2n} = {5}^{4} \\ 2n = 4 \\ n = 2$


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Answer 2

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