I am doing some analysis to calculate the value of log_10(x) which is a negative number. I am now trying to plot these values, however, since the range of the answers is very large I would like to use a logarithmic scale for this. If I simply use plt.yscale('log') I get a message telling me UserWarning: Data has no positive values, and therefore cannot be log-scaled. I also cannot supply the values of x to plt.plot as the result of log_10(x) is so large and negative that the answer of x**(log_10(x)) is simply 0.

What might be the most straightforward way of plotting this data?

You can use

plt.yscale('symlog')

to set the scale to a symmetic log scale. This means that it will scale logarithmically to both sides of 0. Only using the negative part of the symlog scale would work just fine.