Question

25powerx-1=5power(2n-1)-100

Answer 1

${25}^{x - 1} = {5}^{2x - 1} - 100 \\ \\ = > {5}^{2x} \times \frac{1}{25} = {5}^{2x} \times \frac{1}{5} - 100 \\ \\ = > {5}^{2x} ( \frac{1}{25} - \frac{1}{5} ) = - 100 \\ \\ = > {5}^{2x} ( \frac{5 - 25}{125} ) = - 100 \\ \\ = > {5}^{2x} ( \frac{ - 20}{125}) = - 100 \\ \\ = > {5}^{2x} ( \frac{ - 4}{25}) = - 100 \\ \\ = > {5}^{2x} = \frac{100 \times 25}{4} \\ \\ = > {5}^{2x} = 25 \times 25 \\ \\ = > {5}^{2x} = {5}^{4} \\ \\ = > 2 x = 4 \\ \\ = > x = 2$

Answer 2

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