ln( 30.5 )?| Natural (ln) Log Calculator

Here is the answer to questions like: ln( 30.5 )? or How to find the natural log of 30.5?

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

Natural Logarithm Calculator - ln(x)

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

ln(  ) = ?   
Result:
The natural logarithm of 30.5 is 3.4177266836134 or ln(30.5) = 3.4177266836134.
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

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)

nlogennlogennlogennlogen
0.01-4.605170.26-1.347070.51-0.673340.76-0.27443
0.02-3.912020.27-1.309330.52-0.653920.77-0.26136
0.03-3.506550.28-1.272960.53-0.634880.78-0.24846
0.04-3.218870.29-1.237880.54-0.616180.79-0.23572
0.05-2.995730.30-1.203970.55-0.597830.80-0.22314
0.06-2.813410.31-1.171180.56-0.579820.81-0.21072
0.07-2.659260.32-1.139430.57-0.562120.82-0.19845
0.08-2.525730.33-1.108660.58-0.544720.83-0.18633
0.09-2.407940.34-1.078810.59-0.527630.84-0.17435
0.10-2.302580.35-1.049820.60-0.510820.85-0.16252
0.11-2.207270.36-1.021650.61-0.494300.86-0.15082
0.12-2.120260.37-0.994250.62-0.478030.87-0.13926
0.13-2.040220.38-0.967580.63-0.462030.88-0.12783
0.14-1.966110.39-0.941610.64-0.446290.89-0.11653
0.15-1.897120.40-0.916290.65-0.430780.90-0.10536
0.16-1.832580.41-0.891600.66-0.415510.91-0.09431
0.17-1.771960.42-0.867500.67-0.400470.92-0.08338
0.18-1.714800.43-0.814190.68-0.385660.93-0.07257
0.19-1.660730.44-0.820980.69-0.371060.94-0.06187
0.20-1.609440.45-0.798510.70-0.356670.95-0.05129
0.21-1.560650.46-0.776530.71-0.342490.96-0.04082
0.22-1.514120.47-0.755020.72-0.328500.97-0.03046
0.23-1.469680.48-0.733970.73-0.314710.98-0.02020
0.24-1.427110.49-0.713350.74-0.301100.99-0.01005
0.25-1.386290.50-0.692140.75-0.287681.00-0.00000

The natural logarithm table (>= 1.0)

nlogennlogennlogennlogen
1.00.000003.01.098615.01.6094425.03.21887
1.10.095313.11.131406.01.7917626.03.25809
1.20.182323.21.163157.01.9459127.03.29583
1.30.262363.31.193928.02.0794428.03.33220
1.40.336473.41.223779.02.1972229.03.36729
1.50.405463.51.2527610.02.3025830.03.40119
1.60.470003.61.2809311.02.3978940.03.68888
1.70.530633.71.3083312.02.4849150.03.91202
1.80.587793.81.3350013.02.5649560.04.09434
1.90.641853.91.3609714.02.6390570.04.24849
2.00.693144.01.3862915.02.7080580.04.38202
2.10.741934.11.4109916.02.7725990.04.49981
2.20.788454.21.4350817.02.83321100.04.60517
2.30.832914.31.4586118.02.89037200.05.29832
2.40.875474.41.4816019.02.94444300.05.70378
2.50.916294.51.5040820.02.99573400.05.99146
2.60.955514.61.5260521,03.04452500.06.21461
2.70.993254.71.5475622,03.09104600.06.39693
2.81.029624.81.5686123.03.13549700.06.55108
2.91.064714.91.5892324.03.17805800.06.68461

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