Is my solution correct? If formula E=(1.74 x 10^19 x 10^1.44M)

The number 5.21 is correct, though the setting up is confusing.
The actual algebra appears ok.

Usually you dont write decimals for standard form so instead of ....x10^26.2 just write in form ....x10^26

The 1989=5M and 1900=2E was just reference from the question asked…
So, in 1989 the magnitude was 5m and second part in 1900 energy release was 2E from 1989…
Do you think I should remove this to remove any confusion?

E and M are variables defined in the question, yet you seem to be using them as shorthand for energy and magnitude which is not standard, to say the least. It doesnt make sense what youve written. You could say something like
Note the scientific notation mentioned above and yesterday.

I see what you mean, using equal signs could be confusing for the person checking my work.
So, from what I recall yesterday. I had a little trouble trying to understand.
Let’s say, I have this. E=1.74 X 10²⁶ X 10^0.2
How do I find that solution 2.7 x 10²⁶ without using the calculator?

Ah, right, okay.
I suppose because none of my previous tutors has ever said anything. They'd just looked at my main calculations and ignored any side notes that I made, I never really thought about it.

Youre calcs are ok here, though as per yesterday you could simplify the final expression abit as
M = (log(2) + 7.2)/1.44 = 5 + log(2)/1.44
as you have log(2*10^26.2) which can be transformed.

Do you mean part cii?

Yes, you something like
log(4*10^26.2/2) = log(2*10^26.2) = log(2) + 26.2 ....

I was just wondering, for part ci, do you think they may have been looking for me to apply log in order find 26? Or, would it have to hint in some degree by I don’t know, saying simply as far as possible.
I’m concerned as this might be what was intended?