Good evening Candice! I will do this when I return, as I just hopped on my last bus to go home after a 6-hour class.

I will reach home at 1 am and look at the question again at 2 am. First part is easy. Second part I do later.

Now, lg 2020^2020
= 2020 lg 2020
= 2020 * 3.30535...
= 6676.80...

Since n < lg x < n + 1,

6676 < 6676.80... < 6677

This means that 2020^2020 has 6677 digits.

To put it more simply, we use 3^8 for illustration which has an actual value of 6561 or 4 digits long.

log 3^8
= 8 log 3
= 3.8...

Basically, 1000 < 6561 < 10000 leading to 3 < 3.8... < 4. The “4” represents the number of zeroes behind the 1 for 1000...

So 6561 has 4 digits.

As another illustration,

2^6 = 64
10 < 64 < 100
1 < 1.806... < 2

So we round “up” our answer to 2.

omg! I am so sorry to trouble u while u are having your class. Pls take care, Mr Eric. There is no hurry. U can help me when u have time.

Thanks Mr Eric. Yes, 1st part is easy but I am stuck at the 2nd part :(

Good evening Candice! I have updated my chat box as above.

Later I will write up the workings at home around 2 am if I do not get too tired.