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
| 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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