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(52795)   (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).
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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.
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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.
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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).
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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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