code: '''simple docstring'''
  
  
  
  
  
  import math
  
  
  def 					__lowerCAmelCase			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							_lowercase				=	math.log(2 ,10					) * number
  							_lowercase				=	round((log_number - int(_A					)) ,15					)
  
  							return difference
  
  
  def 					__lowerCAmelCase			(  _A = 678_910					):
  
  
  
  							"""simple docstring"""
  
  
  							_lowercase				=	90
  							_lowercase				=	0
  
  							_lowercase				=	math.log(1.2_3 ,10					)
  							_lowercase				=	math.log(1.2_4 ,10					)
  							_lowercase				=	0
  
  							while position < number:
  														_lowercase				=	log_difference(_A					)
  
  														if difference >= upper_limit:
  																					power_iterator += 93
  
  														elif difference < lower_limit:
  																					power_iterator += 196
  
  														else:
  																					_lowercase				=	power_iterator
  																					power_iterator += 196
  																					position += 1
  
  							return previous_power
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  				print(F'''{solution() = }''')
  
  
  
style_context: import math
  from timeit import timeit
  
  
  def 					__lowerCAmelCase			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							_lowercase				=	0
  							_lowercase				=	abs(_A					)
  							while True:
  														_lowercase				=	n // 10
  														digits += 1
  														if n == 0:
  																					break
  							return digits
  
  
  def 					__lowerCAmelCase			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							return 1 if n == 0 else math.floor(math.log(abs(_A					) ,10					) + 1					)
  
  
  def 					__lowerCAmelCase			(  _A					):
  
  
  
  							"""simple docstring"""
  
  
  							return len(str(abs(_A					)					)					)
  
  
  def 					__lowerCAmelCase			(  ):
  
  
  
  							"""simple docstring"""
  
  
  							from collections.abc import Callable
  
  							def benchmark_a_function(_A ,_A					) -> None:
  														_lowercase				=	f'''{func.__name__}({value})'''
  														_lowercase				=	timeit(f'''__main__.{call}''' ,setup="""import __main__"""					)
  														print(f'''{call}: {func(_A					)} -- {timing} seconds'''					)
  
  							for value in (262_144, 1_125_899_906_842_624, 1_267_650_600_228_229_401_496_703_205_376):
  														for func in (num_digits, num_digits_fast, num_digits_faster):
  																					benchmark_a_function(_A ,_A					)
  														print()
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  				benchmark()
  
  
  