ln( 470 )?| Natural (ln) Log Calculator

Natural Logarithm Calculator - ln(x)

Please enter a positive number (x) to calculate ln(x):

ln(  ) = ?   
Result:
The natural logarithm of 470 is 6.1527326947041 or ln(470) = 6.1527326947041.
Notes:
i) e and pi are accepted values.
ii) 1.2 x 103 should be entered as 1.2e3 and
iii) 1.2 x 10-3 as 1.2e-3

Here is the answer to questions like: ln( 470 )? or How to find the natural log of 470?

Use our base e log calculator to find the natural logarithm of any positive real number.

What is natural logarithm?

The natural log is the logarithm to the base of the number e and is the inverse function of an exponential function. Natural logarithm is particular case of logarithms and is typically used in solving time, growth/decay problems.

The number 'e' is an irrational constant approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln(x) or logex.

The natural logarithm of x is the power to which e would have to be raised to equal x. For example, ln(10) is 2.30258509..., because e2.30258509... = 10.

Natural Logarithm Basic Rules

Rule name Rule Example

Product rule

ln(x ∙ y) = ln(x) + ln(y)

ln(53) = ln(5) + ln(3)

Quotient rule

ln(x / y) = ln(x) - ln(y)

ln(5 / 3) = ln(5) - ln(3)

Power rule

ln(x y) = y ∙ ln(x)

ln(35) = 5ln(3)

ln of reciprocal

ln(1/x) = −ln(x)  

ln of negative number

ln(x) is undefined when x ≤ 0  

ln of e

ln(e) = 1  

ln of zero

ln(0) is undefined  

ln of one

ln(1) = 0  

ln of infinity

lim ln(x) = ∞ ,when x→∞  

ln derivative

[ln(x)]' = 1 / x  

ln integral

ln(x)dx = x ∙ (ln(x) - 1) + C  

The natural logarithm table (<= 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 (>= 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

Natural (ln) Log Calculator

Natural (ln) Log Calculator

Please link to this page! Just right click on the above image, choose copy link address, then past it in your HTML.

Disclaimer

While every effort is made to ensure the accuracy of the information provided on this website, neither this website nor its authors are responsible for any errors or omissions. Therefore, the contents of this site are not suitable for any use involving risk to health, finances or property.