The logarithm to base 10 is called the common logarithm

$\log_{x}{8000}=3$

$\implies$ $\text{x}^{3}=8000$ , $\sqrt[3]{8000}=x$

$\sqrt[3]{8000}=20$

$\therefore$ the answer is $\boxed{20}$

Note: for trailling numbers of zero of A number for $\sqrt{}$ or any other root we separate for the value of root the zeros.

For example:

$\sqrt[2]{00}=0$

$\sqrt[2]{0000}=00$

$\vdots$

$\sqrt[3]{000}=0$

$\sqrt[3]{000000}=00$

$\vdots$

For Evaluate the $\sqrt[3]{8000}$ we have $\sqrt[3]{8}=2,{\sqrt[3]{000}=0}$ thus the answer is 20.

$\log_x 8000 = 3 \\ x^3 = 8000 \\ x = \sqrt[3]{8000} \\ x = \boxed{20}$

$\log_x8000 = 3 \\ \log_x20^3 = 3 \\ 3\log_x20=3 \\ \log_x20=1 \\ \therefore x = 20$

$\log_x 8000 = 3$

$\Rightarrow 8000 = x^3$

$\Rightarrow \sqrt[3]{8000} = x$

$\Rightarrow \sqrt[3]{(20^3)} = x$

$\Rightarrow \boxed{20} = x$