Question

How many digits would be in the product of 2x2x2x2x (30 times)?

Answer 1

Use a calculator ................

Answer 2

Answer:

10 Digits

Step-by-step explanation:

Let x = 2 ^ 30 ---------------- ( 2x2x2x2x (30 times))

Taking base 10 logarithm in both sides of equation

log x = log 2 ^ 30

log x = 30 log 2

log x around 30(0.3010)

log x around 9.030

log x = 0.03 + log 10 ^ 9

It means x = A x 10 ^ 9, letting A represents a number that belongs in a Real Number Set

Example if there is 2 x 10 ^ 2 it equals 200 which has 3 digits

3.4 x 10 ^ 3 = 3400 which has 4 digits

it means that A x 10 ^ n will have n + 1 digits

## x will have 9 + 1 = 10 digits