How many digits?
Algebra
Level
3
Given that , how many digits are there in ?
Taken from MTAP Math Challenge Team Orals
The answer is 48.
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1 solution
Used a very basic property of logarithms.....
Here, log 3 = 0.477, in 0.477 , the part to the left of decimal is called Characteristic and to the right is Mantissa
Simple Concept:-- no. of digits = 1+ characteristic (with base 10)
therefore,
log 9^{50} = 50 log 3^{2} = 100 log 3 = 47.7
characteristic = 47
no. of digits = 48