Question

Find the value of x............

Answer 1

${5}^{x} - {5}^{x - 1} = 100 \\ \\ = > {5}^{x} - \frac{ {5}^{x} }{5} = 100 \\ \\ = > {5}^{x} (1 - \frac{1}{5} ) = 100 \\ \\ = > {5}^{x} \times \frac{4}{5} = 100 \\ \\ = > {5}^{x} = \frac{100 \times 5}{4} \\ \\ = > {5}^{x} = 125 \\ \\ = > {5}^{x} = {5}^{3} \\ \\ On \: comparing: \: \\ \\ = > x = 3$

So, the value of x will be 3