Given wavelength

The wavelength is $\lambda = 5800\,\text{\AA}$

Convert angstrom to cm

We know: $1\,\text{\AA} = 10^{-8}\,\text{cm}$

Therefore, $\lambda = 5800 \times 10^{-8}\,\text{cm} = 5.8 \times 10^{-5}\,\text{cm}$

Use formula for wavenumber

Wavenumber is $\bar\nu = \frac{1}{\lambda}$

So, $\bar\nu = \frac{1}{5.8 \times 10^{-5}}\,\text{cm}^{-1}$

Calculate

$\bar\nu = \frac{1}{5.8} \times 10^5$ $\bar\nu \approx 0.1724 \times 10^5 = 1.724 \times 10^4\,\text{cm}^{-1}$

Match with the given form

Given: $\bar\nu = x \times 10\,\text{cm}^{-1}$

So, $1.724 \times 10^4 = x \times 10$

$x = \frac{1.724 \times 10^4}{10} = 1724$

Final answer

$\boxed{1724}$