X isn't a natural number

There are $2$ ways:

Method 1: If $125^{x}=3125$ , $x$ must larger than $1$ , so $\frac{5}{3}$ must be the answer.

Method 2:

$\quad(125)^{x}=3125$

$\Rightarrow 5^{3x}=5^{5}$

$\Rightarrow 3x=5$

$x= \boxed{\frac{5}{3}}$

because it's the only choice which bigger than one

125^x = 3125

Log base(125) 3125 =x

Log base(5^3) 5^5 =x

Therefore x =5/3

$\quad(125)^x=3125$

$\Leftrightarrow 5^{3x}=5^5$

$\Leftrightarrow 3x=5$

$\Leftrightarrow x=\boxed{\dfrac{5}{3}}$

$\displaystyle 125 ^ { x } = 3125 \leftrightarrow ( 5 ^ { 3 } ) ^ { x } = 5 ^ { 5 } \leftrightarrow 5 ^ { 3x } = 5 ^ { 5 } \Leftrightarrow 3x = 5 \Leftrightarrow \boxed { x = \boxed { \frac { 3 } { 5 } } }$ .

The answer is oviously greater than $1$ which is satisfied by only one option which is $\color{#69047E}{\boxed{\dfrac{5}{3}}}$ .

(5³)ˣ = 5⁵ ⇒ 3x = 5 ⇒ x = 5/3

$125^x=5^{3x}$ and $3125=5^5$ $\Rightarrow 5^{3x}=5^5 \Rightarrow (5^{3x})^{\frac{1}{3}}=(5^5)^{\frac{1}{3}} \Rightarrow 5^x=5^{\frac{5}{3}}$

$\therefore \boxed{x=\frac{5}{3}}$