Finance and logs- question

[gus]

By what means does 'log 1.333' equal 0.1248?:o

That's the easier part of your question:
when there's no base specified in the log notation, it means we're using the default base 10 (which most basic scientific calculators can resolve). You can rewrite Log 1.333 = 0.1248 as 10 raised to the power 0.1248 = 1.333

Try it on your windows calculator in scientific mode, input 1.333 and then press the log button.

And by:

1.333 = (1+I)n
log 1.3333 = 4 log (1+I)

I'm guessing by (1+I)n you meant (1+I) raised to power 4 and that there was some sort of typo or an intermediate step is missing that got us from n to 4.

This following link has some clear explanation:
College Algebra Tutorial on Logarithmic Properties

Please let me know if you need further assistance with logs.