Question

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

Answer 1

Solution↷

$25 ^{n - 1} + 100 = 5 ^{2n - 1} \\ 5 {}^{2n - 2} + 100 = 5 {}^{2n - 1} \\ {5}^{2n - 1 - 1} + 100 = 5 {}^{2n - 1} \\ \frac{5 {}^{2n - 1} }{5} + 100 = {5}^{2n - 1} \\ Let \: {5}^{2n - 1} = t \\ \frac{t}{5} + 100 = t \\ \frac{4t}{5} = 100 \\ t = 125 \\ \sf \color{green}So ,\: We \: Get \\ {5}^{2n - 1} = 125 \\ {5}^{2n - 1} = {5}^{3} \\ 2n - 1 = 3 \\ \implies 2n = 4 \\n = 2 \\ \sf \color {lime}Hence, \: the \: Answer \: is \underline{ \: 2}$

Answer 2

Answer:

Step-by-step explanation:

hop it helps maybe not sure .