the numerical value of 3^70 has how many digits?

Question

i really need an answer for this question, and i need to know how to solve this question thanks

Answer 1

Notice:
log(10) = 1
log(100) = 2
log(1000) = 3
log(10000) = 4

Also notice that log(11) through log(99) are all greater than 1, but less than 2. Same holds for log(101) through log(999), etc.

In general if you take log(n) and round down, then add 1, you will get the number of digits.

Using the rule of logs:
log(a^b) = b log(a)

log(3^70) = 70 log(3)
≈ 70 * 0.477121255
≈ 33.3984878

Round down and add 1...
= 33 + 1 = 34 digits

So that tells you 3^70 has 34 digits.

Answer 2

You're supposed to do it w/o evaluating the number.

Use the log at base 10: if a number has n digits (in base 10) then its log is at least n-1 and less than n. In this case,

log(10)3^70 = 70*log(10)3 = 33.398

so it has 34 digits.

Answer 3

You can calculate it by taking logarithm of 3^70.

log(3^70)=70*log(3)=70*0.4771=...

Total number of digits=33+1=34

Answer 4

You can calculate it by taking logarithm of 3^70.

log(3^70)=70*log(3)=70*0.4771=33.398

Total number of digits=33+1=34

Answer 5

If there isn't any reduce on operation symbols, then the most impressive answer is: 999!!!!!!!!!!!!!!!!!!!... with the factorial symbols going out to infinity. therefore, the finest numerical fee you are able to write with 3 digits is infinity. for sure, there are 1000's of alternative ideas to get infinity with 3 digits, yet that's one way.

Answer 6

3^70=2.5031555049932416013155719860858e+33
this number has 34 digits.

Answer 7

2503155504993241601
315571986085849