# 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, $log_{e}$ x, or sometimes, if the base e is implicit, simply log x.

The formula for natural log is given as,

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

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

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

### Natural logarithms table

x ln x
0 undefined
0+ – ∞
0.0001 -9.210340
0.0010 -6.907755
0.0100 -4.605170
0.1000 -2.302585
1.0000 0.000000
2.0000 0.693147
e ≈ 2.7183 1.000000
3.0000 1.098612
4.0000 1.386294
5.0000 1.609438
6.0000 1.791759
7.0000 1.945910
8.0000 2.079442
9.0000 2.197225
10.0000 2.302585
20.0000 2.995732
30.0000 3.401197
40.0000 3.688879
50.0000 3.912023
60.0000 4.094345
70.0000 4.248495
80.0000 4.382027
90.0000 4.499810
100.0000 4.605170
200.0000 5.298317
300.0000 5.703782
400.0000 5.991465
500.0000 6.214608
600.0000 6.396930
700.0000 6.551080
800.0000 6.684612
900.0000 6.802395
1000.0000 6.907755
10000.0000 9.210340
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