The raster calculator is one of the most flexible and versatile tools in QGIS. This allows you to perform algebraic operations based on raster layers, and compute new layers. This recipe shows you how to use it.

catchment_area layer. Select this layer.ln(a).
The layers selected in the layer selector are referred to using a single letter in alphabetical order (a for the first one, b for the second one, and so on). In this case, we selected just one layer, so we can refer to it as a in the formula.
The formula calculates a natural logarithm of the values in the catchment area layer. The distribution of values in this layer is not homogeneous because it contains a large number of cells with low values and just a few of them with very large values. This causes the rendering of the layer to be not very informative with most of the colors in the color ramp not even being used.
The resulting layer is much more informative because applying the logarithm alters the distribution of values, resulting in a more explicit rendering.
QGIS contains a raster calculator module outside of Processing. You can find this by navigating to Raster | Raster calculator...:

This interface resembles an actual calculator, and it is more intuitive and user friendly. On the other hand, this lacks many of the functions that are available in the Processing raster calculator (the logarithm that we have computed, for instance, is not available). This also cannot be used in automated processes, such as scripts or graphical models, which are only available for the Processing algorithms.
On the other hand, the QGIS built-in calculator supports multiband layers, while the Processing one is limited to single-band ones.