An alternative approach.

Here, both lg and ln work perfectly fine! Ln can also be used here.

For e^(3x - 1) = 8, there is nothing wrong with using lg to solve it, while for 10^(3x - 1) = 8, there is nothing wrong with using ln to solve it (if calculators can calculate logs to other bases also, it would also be allowed).

But e is commonly paired with ln because ln e = 1 as part of the workings and this simplifies our calculations a little.

Which is why ln is commonly applied to e and lg is commonly applied to 10.