Given two positive integers a and b, task is to find the number of digits in a^b (a raised to the power b).
Input: a = 2 b = 5 Output: no. of digits = 2 Explanation: 2^5 = 32 Hence, no. of digits = 2 Input: a = 2 b = 100 Output: no. of digits = 31 Explanation: 2^100 = 1.2676506e+30 Hence, no. of digits = 31
The number of digits in a^b can be calculated using the formula:
Number of Digits = 1 + b * (log10a)
When a number is divided by 10, it is reduced by 1 digit.
554 / 10 = 55, 55 / 10 = 5
Notice, 554 initially has 3 digits but after division there are 2 digits 55 and after further division there is only 1 digit 5. So it can be concluded that to count number of digits, how many times a number is divided by 10 to reach 1 needs to be calculated.
log base 10 of a number is the number of times a number needs to be divided by 10 to reach 1 but as 1 itself is not included in log base 10, 1 is added to get the number of digits.
Note: Floor value of b * (log10a) is taken.
Below is the implementation to calculate the number of digits in a^b.
no.of digits = 31
- Check whether product of digits at even places is divisible by sum of digits at odd place of a number
- Maximize the given number by replacing a segment of digits with the alternate digits given
- Count of numbers between range having only non-zero digits whose sum of digits is N and number is divisible by M
- Find smallest number with given number of digits and sum of digits
- Find the Largest number with given number of digits and sum of digits
- Minimum number of digits to be removed so that no two consecutive digits are same
- Smallest number with given sum of digits and sum of square of digits
- Number of digits in the nth number made of given four digits
- Number of digits to be removed to make a number divisible by 3
- Find the smallest number whose digits multiply to a given number n
- Number of times a number can be replaced by the sum of its digits until it only contains one digit
- Find count of digits in a number that divide the number
- Find maximum number that can be formed using digits of a given number
- Print a number strictly less than a given number such that all its digits are distinct.
- Count number of digits after decimal on dividing a number
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