LogMior1.rtf p1 of 2
Deriving Logarithms Without A Calculator
This algorithm developed by Michael Mior of the Rochester Institute of Technology
determines Base 10 logarithms without a calculator. Note that this system works
for any base but the example here is for log10 values.
Overview:
n =number whose log is desired
n1 =n
1.) Determine the highest power of 10 [10x] which doesn't exceed n1
This exponent (x) will be the first value of log10 (n).
2.)Divide n1 by 10x [ n1 =n1 / 10x ] .
3.)Raise n1 to n110
4.)Determine the highest power of 10 [10x] which doesn't exceed n1.
This exponent (x)becomes the next number in the log.
5.)Repeat steps 2-4 until the required precision is reached.
Example: Find the logarithm of 876
n = 876
n1 =n =876
1.) Determine the highest power of 10 which doesn't exceed n1
100 [ 102 ] is the nearest power of 10 which doesn't exceed 876. The exponent (2)
becomes the first number of the log.
Log10 876 =2.xxx
2.Divide n1 by 102 .
876 / 102 =8.76
n1 =8.76
3.)Raise n1 to n110 [n1 =n110 ]
8.7610 =2660976638
n1 =2660976638
4.)Determine the highest power of 10 which doesn't exceed n1
109 =1 000 000 000
This exponent [ 9 ] becomes the next number in the log.
Log10 876 =2.9xx
Repeat steps 2-4
2.)Divide n1 by 109 [ from step 4 previous ]
2660976638 / 109 =2.660976638
n1 =2.660976638
3.)Raise n1 to n110 [ n1 =n110 ]
2.66097663810 =17799.61533
n1 =17799.61533
4.)Determine the highest power of 10 which doesn't exceed n1
104 =10 000
This exponent [ 4 ] becomes the next number in the log.
Log10 876 =2.94x
LogMior1.rtf p2 of 2
Repeat steps 2-4
2.)Divide n1 by 104 [ from step 4 previous ]
17799.61533 /10000 =17.79961533
n1 =17.79961533
3.)Raise n1 to n110 [ n1 =n110 ]
1.77996153310 =319.2318157
n1 =319.2318157
4.)Determine the highest power of 10 which doesn't exceed n1
102 =100
This exponent [ 2 ] becomes the next number in the log.
Log10 876 =2.942
Calculation on a TI-34 for log10 876 =2.942504106
( . . . Cook until done . . .)
afk December 13, 2023
afk March 31, 2024