Question

Please Solve it quickly!!!!

Answer 1

Question :-

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

So,

$= > 100 = {5}^{2x - 1} - {25}^{x - 1}$
now 25 = 5²

=>
$100 = {5}^{2x - 1} - ( {5}^{2} ) {}^{x - 1}$

$= > 100 = {5}^{2x - 1} - {5}^{2x - 2}$

Now
${5}^{2x} - 1 = \frac{ {5}^{2x} }{5} \\ \\ and \: {5}^{2x - 2} = \frac{ {5}^{2x} }{ {5}^{2} }$


=>
$100 = \frac{ {5}^{2x} }{5} - \frac{ {5}^{2x} }{ {5}^{2} } \\ \\ = > 100 = {5}^{2x} ( \frac{1}{5} - \frac{1}{25} ) \\ \\ = > 100 = {5}^{2x} ( \frac{5}{25} - \frac{1}{25} ) \\ \\ = > 100 = {5}^{2x} ( \frac{4}{25} ) \\ \\ = > {5}^{2x} = 100 \times \frac{25}{4} \\ \\ = > {5}^{2x} = 25 \times 25 \\ \\ = > {5}^{2x} = {5}^{2} \times {5}^{2} \\ \\ = > {5}^{2x} = {5}^{4} \\ \\ = > 2x = 4 \\ \\ (by \: comparing \: the \: bases) \\ \\ = > x = \frac{4}{2} \\ \\ = > x = 2$


Answer :- 2