Natural Logarithms
17
find the value of V that has this log. The mantissa 0.2655 lies in the row corresponding to 1.8, between the columns headed 4 and 5. In fact 0.2655 is 7/24, or
approximately 0.3, of the way between 0.2648 and 0.2672. Therefore the number
corresponding to I0
02l) " is 1.843, and the number we seek is 1.843 x I0~
7 .
NATURAL LOGARITHMS
Numbers other than 10 could be used as the base for logarithms, but the only
other base that is commonly used is e , an inexact number (like TT) that has
mathematical significance. Many laws of chemistry and physics are derived
mathematically from physical models and principles and, as a result, involve
logarithms with the base e . These logarithms are called natural logs. The natural log of a number N is abbreviated In N. The value of e is 2.71828183. . . .
You can always convert common logs to natural logs (or vice versa) if you know
the conversion factor of 2.30258509 . . . (usually rounded to 2.303) and employ it in one of the following ways:
\ = In N = 2.303 log N
Some calculators can provide natural logs directly, without any need to convert
explicitly from one form to the other. If your calculator has this capability, you
would simply enter through the keyboard the number whose natural log you
desire, then press the natural log key (or keys), whose symbol is probably LN.
On your own calculator you can check that In 4762 = 8.46842, and that
In 0.0000765 = -9.47822.
Most calculators have a means of providing the antilns of natural logs, as
follows.
1. Enter the given log through the keyboard. Use the "change sign" key
after entry if the log is negative; don't use the — key (i.e., the subtract
key).
2. Press the antiln key (or keys). On an HP-type calculator, a common
key symbol is <
x ; on a Tl-type calculator you would usually press the
INV and LNykeys, in that order.
3. The antiln appears in the lighted display.
Using your own calculator, make sure that you can find the following antilns:
antiln 1.09861 = 3.00000; antiln 13.47619 = 7.12254 x 10
5
, and antiln
(-7.60354) = 4.98683 x 10~
4 .
17
find the value of V that has this log. The mantissa 0.2655 lies in the row corresponding to 1.8, between the columns headed 4 and 5. In fact 0.2655 is 7/24, or
approximately 0.3, of the way between 0.2648 and 0.2672. Therefore the number
corresponding to I0
02l) " is 1.843, and the number we seek is 1.843 x I0~
7 .
NATURAL LOGARITHMS
Numbers other than 10 could be used as the base for logarithms, but the only
other base that is commonly used is e , an inexact number (like TT) that has
mathematical significance. Many laws of chemistry and physics are derived
mathematically from physical models and principles and, as a result, involve
logarithms with the base e . These logarithms are called natural logs. The natural log of a number N is abbreviated In N. The value of e is 2.71828183. . . .
You can always convert common logs to natural logs (or vice versa) if you know
the conversion factor of 2.30258509 . . . (usually rounded to 2.303) and employ it in one of the following ways:
\ = In N = 2.303 log N
Some calculators can provide natural logs directly, without any need to convert
explicitly from one form to the other. If your calculator has this capability, you
would simply enter through the keyboard the number whose natural log you
desire, then press the natural log key (or keys), whose symbol is probably LN.
On your own calculator you can check that In 4762 = 8.46842, and that
In 0.0000765 = -9.47822.
Most calculators have a means of providing the antilns of natural logs, as
follows.
1. Enter the given log through the keyboard. Use the "change sign" key
after entry if the log is negative; don't use the — key (i.e., the subtract
key).
2. Press the antiln key (or keys). On an HP-type calculator, a common
key symbol is <
x ; on a Tl-type calculator you would usually press the
INV and LNykeys, in that order.
3. The antiln appears in the lighted display.
Using your own calculator, make sure that you can find the following antilns:
antiln 1.09861 = 3.00000; antiln 13.47619 = 7.12254 x 10
5
, and antiln
(-7.60354) = 4.98683 x 10~
4 .