Question

please solve this problem...​

Answer 1

Answer:

The answer is x = (1 / 2).

Step-by-step explanation:

The explanation for the answer is given as follows.

$125 ^ x = \frac{25}{5^x}$

Multiplying both sides by $5^x$

$125 ^x * 5 ^x$ = 25

Taking, $x$th root on both sides.

$\sqrt[x]{125 ^ x * 5 ^ x}$ = $\sqrt[x]{25}$

The roots cancel each other on left side.

125 * 5 = $\sqrt[x]{25}$

625 = $\sqrt[x]{25}$

We know that, $25 ^ 2$ = 625, But 625 = $\sqrt[x]{25}$.

Hence, $25^2 = \sqrt[x]{25}$

Also, $\sqrt[x]{25}$ can be written as $25 ^ \frac{1}{x}$

So, $25^2 = 25^\frac{1}{x}$

Hence, 2 = $\frac{1}{x}$

x = $\frac{1}{2}$, So proved.

Have a good day.

Answer 2

Step-by-step explanation:

$\rm {125}^{x} = \frac{25}{ {5}^{x} }$

$\rm ({ {5}^{3} })^{x} \times {5}^{x} = {5}^{2}$

$\rm{5}^{3x} \times {5}^{x} = {5}^{2}$

$\rm {5}^{3x + x} = {5}^{2}$

$\rm {5}^{4x} = {5}^{2}$

Comparing the powers,

$\rm4x = 2$

$\rm x = \frac{ \cancel2}{\cancel4}$

$\rm x = \frac{1}{2}$

I hope it is helpful