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Logarithm Table
|
Logarithm Table |
Natural logarithm
When using the component of the capacitor and so on with
the electronic circuits,
the logarithm must be computed to look for the
electric current which flows through the circuit.
The logarithm computation
can be computed with the function computer but I show the tables of logarithm in
this page.
The formula is shown below and it looks for the X.
e is the
base of the natural logarithm and the value is 2.71828.
n
= ex
It becomes the following when changing
into the formula which looks for the X.
x =
logen
So as not to confuse with the
common logarithm("log10" or it is simply expressed with
"log"),
"loge" is sometimes expressed with the "ln".
x = ln n
In case of n=1, it becomes x=0
and when the n is less than 1, x becomes the negative value.
When the n is
less than 1, it becomes the same as the one to have made x which is due to the
value of 1/n negative.
The natural logarithm
table (Equal to or less than 1.0)
| n | logen |  |
n | logen | |
n | logen | |
n | logen |
|---|---|---|---|---|---|---|---|---|---|---|
| 0.01 | -4.60517 | 0.26 | -1.34707 | 0.51 | -0.67334 | 0.76 | -0.27443 | |||
| 0.02 | -3.91202 | 0.27 | -1.30933 | 0.52 | -0.65392 | 0.77 | -0.26136 | |||
| 0.03 | -3.50655 | 0.28 | -1.27296 | 0.53 | -0.63488 | 0.78 | -0.24846 | |||
| 0.04 | -3.21887 | 0.29 | -1.23788 | 0.54 | -0.61618 | 0.79 | -0.23572 | |||
| 0.05 | -2.99573 | 0.30 | -1.20397 | 0.55 | -0.59783 | 0.80 | -0.22314 | |||
| 0.06 | -2.81341 | 0.31 | -1.17118 | 0.56 | -0.57982 | 0.81 | -0.21072 | |||
| 0.07 | -2.65926 | 0.32 | -1.13943 | 0.57 | -0.56212 | 0.82 | -0.19845 | |||
| 0.08 | -2.52573 | 0.33 | -1.10866 | 0.58 | -0.54472 | 0.83 | -0.18633 | |||
| 0.09 | -2.40794 | 0.34 | -1.07881 | 0.59 | -0.52763 | 0.84 | -0.17435 | |||
| 0.10 | -2.30258 | 0.35 | -1.04982 | 0.60 | -0.51082 | 0.85 | -0.16252 | |||
| 0.11 | -2.20727 | 0.36 | -1.02165 | 0.61 | -0.49430 | 0.86 | -0.15082 | |||
| 0.12 | -2.12026 | 0.37 | -0.99425 | 0.62 | -0.47803 | 0.87 | -0.13926 | |||
| 0.13 | -2.04022 | 0.38 | -0.96758 | 0.63 | -0.46203 | 0.88 | -0.12783 | |||
| 0.14 | -1.96611 | 0.39 | -0.94161 | 0.64 | -0.44629 | 0.89 | -0.11653 | |||
| 0.15 | -1.89712 | 0.40 | -0.91629 | 0.65 | -0.43078 | 0.90 | -0.10536 | |||
| 0.16 | -1.83258 | 0.41 | -0.89160 | 0.66 | -0.41551 | 0.91 | -0.09431 | |||
| 0.17 | -1.77196 | 0.42 | -0.86750 | 0.67 | -0.40047 | 0.92 | -0.08338 | |||
| 0.18 | -1.71480 | 0.43 | -0.81419 | 0.68 | -0.38566 | 0.93 | -0.07257 | |||
| 0.19 | -1.66073 | 0.44 | -0.82098 | 0.69 | -0.37106 | 0.94 | -0.06187 | |||
| 0.20 | -1.60944 | 0.45 | -0.79851 | 0.70 | -0.35667 | 0.95 | -0.05129 | |||
| 0.21 | -1.56065 | 0.46 | -0.77653 | 0.71 | -0.34249 | 0.96 | -0.04082 | |||
| 0.22 | -1.51412 | 0.47 | -0.75502 | 0.72 | -0.32850 | 0.97 | -0.03046 | |||
| 0.23 | -1.46968 | 0.48 | -0.73397 | 0.73 | -0.31471 | 0.98 | -0.02020 | |||
| 0.24 | -1.42711 | 0.49 | -0.71335 | 0.74 | -0.30110 | 0.99 | -0.01005 | |||
| 0.25 | -1.38629 | 0.50 | -0.69214 | 0.75 | -0.28768 | 1.00 | -0.00000 |
The natural logarithm table
(Equal to or more than 1.0)
| n | logen | |
n | logen | |
n | logen | |
n | logen |
|---|---|---|---|---|---|---|---|---|---|---|
| 1.0 | 0.00000 | 3.0 | 1.09861 |
5.0 |
1.60944 |
25.0 |
3.21887 | |||
| 1.1 | 0.09531 | 3.1 | 1.13140 |
6.0 |
1.79176 |
26.0 |
3.25809 | |||
| 1.2 | 0.18232 | 3.2 | 1.16315 |
7.0 |
1.94591 |
27.0 |
3.29583 | |||
| 1.3 | 0.26236 | 3.3 | 1.19392 |
8.0 |
2.07944 |
28.0 |
3.33220 | |||
| 1.4 | 0.33647 | 3.4 | 1.22377 |
9.0 |
2.19722 |
29.0 |
3.36729 | |||
| 1.5 | 0.40546 | 3.5 | 1.25276 | 10.0 | 2.30258 |
30.0 |
3.40119 | |||
| 1.6 | 0.47000 | 3.6 | 1.28093 | 11.0 | 2.39789 |
40.0 |
3.68888 | |||
| 1.7 | 0.53063 | 3.7 | 1.30833 | 12.0 | 2.48491 |
50.0 |
3.91202 | |||
| 1.8 | 0.58779 | 3.8 | 1.33500 | 13.0 | 2.56495 |
60.0 |
4.09434 | |||
| 1.9 | 0.64185 | 3.9 | 1.36097 | 14.0 | 2.63905 |
70.0 |
4.24849 | |||
| 2.0 | 0.69314 | 4.0 | 1.38629 | 15.0 | 2.70805 |
80.0 |
4.38202 | |||
| 2.1 | 0.74193 | 4.1 | 1.41099 | 16.0 | 2.77259 |
90.0 |
4.49981 | |||
| 2.2 | 0.78845 | 4.2 | 1.43508 | 17.0 | 2.83321 | 100.0 | 4.60517 | |||
| 2.3 | 0.83291 | 4.3 | 1.45861 | 18.0 | 2.89037 | 200.0 | 5.29832 | |||
| 2.4 | 0.87547 | 4.4 | 1.48160 | 19.0 | 2.94444 | 300.0 | 5.70378 | |||
| 2.5 | 0.91629 | 4.5 | 1.50408 | 20.0 | 2.99573 | 400.0 | 5.99146 | |||
| 2.6 | 0.95551 | 4.6 | 1.52605 | 21,0 | 3.04452 | 500.0 | 6.21461 | |||
| 2.7 | 0.99325 | 4.7 | 1.54756 | 22,0 | 3.09104 | 600.0 | 6.39693 | |||
| 2.8 | 1.02962 | 4.8 | 1.56861 | 23.0 | 3.13549 | 700.0 | 6.55108 | |||
| 2.9 | 1.06471 | 4.9 | 1.58923 | 24.0 | 3.17805 | 800.0 | 6.68461 |
At the electronic circuits, the common logarithm(the
logarithm having base 10) is used for the thing except above-mentioned natural
logarithm.
n =
10x
x =
log10n
This value is used when it
expresses the mu factor and so on and compares the two values.
The common
logarithm is used for the dB ( decibel ).
The noise to the electric signal
sometimes show the 1/1000 or 1/10000 values and so on.
It shows in the dB
because the number of the figures increases when displaying just as it
is.
In case of the voltage ratio : dB = 20
log10 (V1/V2)
In case of the electric
power ratio : dB = 10 log10 (P1/P2)
It
represents as -60 dB in case of V1=0.001 V , V2=1 V.
When the voltage
ratio is twice, it is 6 dB.
When the electric power ratio is twice, it is 3
dB.
The common logarithm table
| n | log10n | |
n | log10n | |
n | log10n | |
n | log10n |
|---|---|---|---|---|---|---|---|---|---|---|
| 0.0001 | -4.00000 | 1.0 | 0.00000 | 3.0 | 0.47712 | 5.0 | 0.69897 | |||
| 0.001 | -3.00000 | 1.1 | 0.04139 | 3.1 | 0.49136 | 5.1 | 0.70757 | |||
| 0.01 | -2.00000 | 1.2 | 0.07918 | 3.2 | 0.50515 | 5.2 | 0.71600 | |||
| 0.02 | -1.69897 | 1.3 | 0.11394 | 3.3 | 0.51851 | 5.3 | 0.72427 | |||
| 0.03 | -1.52287 | 1.4 | 0.14612 | 3.4 | 0.53148 | 5.4 | 0.73239 | |||
| 0.04 | -1.39794 | 1.5 | 0.17609 | 3.5 | 0.54406 | 5.5 | 0.74036 | |||
| 0.05 | -1.30103 | 1.6 | 0.20412 | 3.6 | 0.55630 | 5.6 | 0.74819 | |||
| 0.06 | -1.22184 | 1.7 | 0.23045 | 3.7 | 0.56820 | 5.7 | 0.75587 | |||
| 0.07 | -1.15490 | 1.8 | 0.25527 | 3.8 | 0.57978 | 5.8 | 0.76342 | |||
| 0.08 | -1.09691 | 1.9 | 0.27875 | 3.9 | 0.59106 | 5.9 | 0.77085 | |||
| 0.09 | -1.04575 | 2.0 | 0.30103 | 4.0 | 0.60206 | 6.0 | 0.77815 | |||
| 0.1 | -1.00000 | 2.1 | 0.32222 | 4.1 | 0.61278 | 6.1 | 0.78533 | |||
| 0.2 | -0.69897 | 2.2 | 0.34242 | 4.2 | 0.62325 | 6.2 | 0.79239 | |||
| 0.3 | -0.52288 | 2.3 | 0.36172 | 4.3 | 0.63347 | 6.3 | 0.79934 | |||
| 0.4 | -0.39794 | 2.4 | 0.38021 | 4.4 | 0.64345 | 6.4 | 0.80618 | |||
| 0.5 | -0.30103 | 2.5 | 0.39794 | 4.5 | 0.65321 | 6.5 | 0.81291 | |||
| 0.6 | -0.22184 | 2.6 | 0.41497 | 4.6 | 0.66275 | 6.6 | 0.81954 | |||
| 0.7 | -0.15490 | 2.7 | 0.43136 | 4.7 | 0.67210 | 6.7 | 0.82607 | |||
| 0.8 | -0.09691 | 2.8 | 0.44715 | 4.8 | 0.68124 | 6.8 | 0.83251 | |||
| 0.9 | -0.04575 | 2.9 | 0.46239 | 4.9 | 0.69019 | 6.9 | 0.83885 |
| n | log10n | |
n | log10n | |
n | log10n |
|---|---|---|---|---|---|---|---|
| 7.0 | 0.84509 | 9.0 | 0.95424 |
20.0 |
1.30103 | ||
| 7.1 | 0.85126 | 9.1 | 0.95904 |
21.0 |
1.32221 | ||
| 7.2 | 0.85733 | 9.2 | 0.96379 |
22.0 |
1.34242 | ||
| 7.3 | 0.86332 | 9.3 | 0.96848 |
23.0 |
1.36172 | ||
| 7.4 | 0.86923 | 9.4 | 0.97312 |
24.0 |
1.38021 | ||
| 7.5 | 0.87506 | 9.5 | 0.97772 |
25.0 |
1.39794 | ||
| 7.6 | 0.88081 | 9.6 | 0.98227 |
26.0 |
1.41497 | ||
| 7.7 | 0.88649 | 9.7 | 0.98677 |
27.0 |
1.43136 | ||
| 7.8 | 0.89209 | 9.8 | 0.99122 |
28.0 |
1.44715 | ||
| 7.9 | 0.89762 | 9.9 | 0.99563 |
29.0 |
1.46239 | ||
| 8.0 | 0.90309 | 10.0 | 1.00000 |
30.0 |
1.47711 | ||
| 8.1 | 0.90848 | 11.0 | 1.04139 |
40.0 |
1.60206 | ||
| 8.2 | 0.91381 | 12.0 | 1.07918 |
50.0 |
1.69897 | ||
| 8.3 | 0.91907 | 13.0 | 1.11394 |
60.0 |
1.77815 | ||
| 8.4 | 0.92428 | 14.0 | 1.14612 |
70.0 |
1.84509 | ||
| 8.5 | 0.92941 | 15.0 | 1.17609 |
80.0 |
1.90309 | ||
| 8.6 | 0.93450 | 16.0 | 1.20142 |
90.0 |
1.95424 | ||
| 8.7 | 0.93952 | 17.0 | 1.23044 |
100.0 |
2.00000 | ||
| 8.8 | 0.94448 | 18.0 | 1.25527 |
1000.0 |
3.00000 | ||
| 8.9 | 0.94939 | 19.0 | 1.27875 | 10000.0 | 4.00000 |
