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Just P&P (Posted on 2011-01-23) Difficulty: 3 of 5
No calculator, no tables-
Please evaluate lg 7 within .01.

Rem: lg 7 is a decimal (by base 10) logarithm of 7.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

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Another way - without remembering any irrational logarithms | Comment 4 of 6 |
With paper and pencil, make a table of 7^n, n being all positive integers.  Look for 7^n being close to a power of 10 for a somewhat large exponent.  7^19 fits this quite well = 113988951853731, which is just greater than 10^16.  (Whew).  While y=log(x) is not asymptotic, its slope is monotonically decreasing, so one can approximate the log(7^19) by log (10^16)=16.  Calculate 16/19=0.842185 to six digits (by long division).  This is within 0.003 of the exact answer.

Edited on January 23, 2011, 3:01 pm

Edited on January 23, 2011, 3:03 pm
  Posted by Kenny M on 2011-01-23 14:56:37

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