Julia plots: Labels in scientific notation as in default font

I have a log log plot and want to change the x-axis labels manually as in the code below. Hence, I need to use powers of 10 – however, the only ways I come up with gives different fonts than the default:

Note that both labels on the x axis have a different font than on the y-axis. The 10^0 is a bit more subtle, but the powers is different and this becomes more noticeable for other powers.
Many thanks in advance!

Here is the code:

using Plots
using LaTeXStrings


# get some random data
myplot = plot(1:40, 1:40, xaxis=:log10, yaxis=:log10, 
            xticks = ([1,2,10],["10⁰",L"$2\times 10^0$","10"]))

plot!(myplot, size=(800,400))

What I do is usually the opposite:

Try also the pgfplotsx() backend:

using LaTeXStrings, Plots; pgfplotsx()
p = plot(1:40, 1:40, axis=:log10, xticks=([1,2,10],[L"10^0",L"$2\times 10^0$","10"]));
plot!(p, size=(800,400))