# Logarithms in uncertainties

I'm looking at the following plot:

The vertical lines show the upper and lower frequency bounds for each of the bands W4, W3, W2...and I'm trying to convert them to wavelengths using $$\lambda=\frac{c}{\nu}$$ so that I can show a similar plot, only in wavelength space, rather than frequency.

As an example, I know that $$\lambda_{W4}=22\mu$$m, so $$f_{W4}=1.36\times10^{13}$$ Hz. What I can't figure out, is the uncertainties in the graph. It's stated in the caption that the frequency bands are $$\Delta log_{10}=\pm 0.05$$, but I'm not sure how to find the bounds from that. Is it:

$$1.36\times 10^{13} \pm log_{10}0.05 = 1.35999\times 10^{13} \rightarrow 1.3600003\times 10^{13}$$

or

$$log_{10}(1.36\times 10^{13} \pm 0.05) = 13.08 \rightarrow 13.63$$ $$=1.2023\times 10^{13} \rightarrow 1.3599\times 10^{13}$$

or am I completely off track?

I would interpret $$\Delta\log_{10}\nu=\pm 0.05$$ in the following way.
$$\Delta\log_{10}\nu=+ 0.05= \log_{10} \nu_{\rm upper} - \log_{10} \nu_{\rm W4}$$ and $$\Delta\log_{10}\nu=- 0.05= \log_{10} \nu_{\rm lower} - \log_{10} \nu_{\rm W4}$$
Knowing $$\nu_{\rm W4}$$ you can find $$\nu_{\rm upper}$$ and $$\nu_{\rm lower}$$ and hence $$\lambda_{\rm lower}$$ and $$\lambda_{\rm upper}$$.