SOLUTION: Without using tables, show that log base 10 of 17 is approximately equal to (2log base 10 of 6 + 3log base 10 of 2).

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Question 1188333: Without using tables, show that log base 10 of 17 is approximately equal to (2log base 10 of 6 + 3log base 10 of 2).
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
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Without using tables, show that log base 10 of 17 is approximately equal to (2log base 10 of 6 + 3log base 10 of 2).
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The statement in your post is  FATALLY  INCORRECT. 

    log(17)      = 1.230  (with 3 decimals after the decimal point)


    2*log(6) + 3*log(2) = 2.460.


    They are not " approximately equal ", in common understanding of used words.

Solved and refuted.


///////////////


Hey,  are you heavily seek by posting this   G I B B E R I S H   ?


I have very effective medicine against such a disease: 

    If I see one more such gibberish posted to the forum,

    I will write to the managers of this project, 

    asking them to remove you from your position in this project.


\\\\\\\\\\\\\\\


As I see from the  Alan's post,  he tries to convert everything to a joke.


Therefore,  I see a necessity to explain,  what the words  " approximately equal "  do really mean.


They mean that the difference between two values is a  "tiny part"  of their magnitudes  (absolute values),
which is,  OBVIOUSLY,  not the case in this problem.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Without using tables, show that log base 10 of 17 is approximately equal to (2log base 10 of 6 + 3log base 10 of 2).
===================
log(17) = ~1.23
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(2log base 10 of 6 + 3log base 10 of 2).
2log(6) + 3log(2) = log(36) + log(8) = log(288) = ~2.459
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"Approximately" can be a matter of opinion.
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PS No tables were used. I used a calculator, a desk and a chair.
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