Question 254177: 13. Natural Logarithm There is a key on your calculator labeled ln. The “l” is for “logarithm,” and the “n” is for “natural” or “Naperian,” after the Scottish mathematician John Napier, who lived in the 1600’s. The two letters are pronounced separately: “ln x” is pronounced “ell n of x.”
a. Find ln 2 and ln 3.
b. One of the special properties of logarithms is that . So if you can find a number b for which that number is the base of natural logarithms. Find an approximation for this base correct to 3 decimal places.
c. The base of natural logarithms is a transcendental number called e. To find a more precise value of e, enter 1 in your calculator, then press the key. What do you get? Your answer in part (b) should be close to this value.
Found 2 solutions by JimboP1977, stanbon:
Answer by JimboP1977(311)   (Show Source):
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Natural Logarithm There is a key on your calculator labeled ln.
The “l” is for “logarithm,” and the “n” is for “natural” or “Naperian,” after the Scottish mathematician John Napier, who lived in the 1600’s.
The two letters are pronounced separately: “ln x” is pronounced “ell n of x.”
a. Find ln 2 and ln 3.
ln(2) = 0.6931472.....
ln(3) = 1.0986123...
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b. One of the special properties of logarithms is that . So if you can find a number b for which that number is the base of natural logarithms. Find an approximation for this base correct to 3 decimal places.
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Words are missing from your post.
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c. The base of natural logarithms is a transcendental number called e. To find a more precise value of e, enter 1 in your calculator, then press the key. What do you get? Your answer in part (b) should be close to this value.
e = 2.718281828450045.....
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Cheers,
Stan H.
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