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# Natural Log Formula

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.

The formula for natural log is given as,

$\large Product\;Rule: ln(xy)=ln(x)+ln(y)$

$\large Quotient\;Rule: ln\left(\frac{x}{y}\right)=ln(x)-ln(y)$

$\large Power\;Rule: ln\left(x^{n}\right)=n ln(x)$

### Natural logarithms table

xln x
0undefined
0+– ∞
0.0001-9.210340
0.0010-6.907755
0.0100-4.605170
0.1000-2.302585
1.00000.000000
2.00000.693147
e ≈ 2.71831.000000
3.00001.098612
4.00001.386294
5.00001.609438
6.00001.791759
7.00001.945910
8.00002.079442
9.00002.197225
10.00002.302585
20.00002.995732
30.00003.401197
40.00003.688879
50.00003.912023
60.00004.094345
70.00004.248495
80.00004.382027
90.00004.499810
100.00004.605170
200.00005.298317
300.00005.703782
400.00005.991465
500.00006.214608
600.00006.396930
700.00006.551080
800.00006.684612
900.00006.802395
1000.00006.907755
10000.00009.210340