Question

5^2 / 10 =2500 / x then x =?​

Answer 1

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$\large\bf{\underline{\red{VERIFIED✔}}}$

The correct problem is given here. there is no leading - in the beginning.

$\begin{gathered} + 5^{2x-1} - 25^{x-1} =2500 \\ \\ + 5^{2x-1} - 5^{2x-2} = 5^2 * 25 * 4\\ \\ + 5^{2x-1} [1 - 5^{-1}] = 5^4 * 2^2 \\ \\5^{(2x-1)} \frac{4}{5} = 5^4 2^2 \\ \\ 5^{2x-1} = 5^5 \\ 2x -1 = 5 \\ x = 3 \\ \end{gathered}$

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Answer 2

$the \: answer \: is \: \boxed {x = 3}$

Step-by-step explanation:

${5}^{2x - 1} - {25}^{x - 1} = 2500$

${5}^{2x - 1} - {5}^{2x - 2} = 2500$

${5}^{2x - 1} (1 - {5}^{ - 1} ) = {5}^{2} ∗ 25∗4$

${5}^{(2x - 1)} \frac{4}{5} = {5}^{4} ∗ {2}^{2}$

${5}^{(2x - 1)} = {5}^{4} {2}^{2} \times \frac{5}{4}$

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

$2x - 1 = 5$

$2x = 6$

$x = 3$