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

Question

i really need an answer for 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

3^70=2.5031555049932416013155719860858e+33
34 digits.

Answer 3

2503155504993241601
315571986085849