Syntax
LN(number)
| Parameter | Description |
|---|---|
| number | Parameter of the LN function. |
Examples
Natural log of e
Formula
=LN(EXP(1))
Returns 1. The natural log of e is 1, since e^1 = e.
Continuous growth rate
Formula
=LN(2)
Returns ~0.6931. At a continuous growth rate of 69.31%, a quantity doubles. This is the basis of the 'Rule of 70' in finance.
Time to double
Formula
=LN(2)/0.07
Returns ~9.9. At 7% continuous growth, it takes about 10 periods to double (the Rule of 70: 70/7 ≈ 10).
Common Errors
#NUM!
LN requires a positive argument. =LN(0) and =LN(-5) both return #NUM! because logarithms of zero and negative numbers are undefined.
#VALUE!
Non-numeric input returns #VALUE!.
Tips
Log returns in finance
Log return = LN(ending_price / starting_price). Log returns are additive across time periods, making them easier to work with than simple returns.
Convert to other bases
LN is base-e. For base-10, use LOG10. For any base: log_b(x) = LN(x)/LN(b). Or just use the LOG function.
Linearizing exponential data
If your data follows y = a×e^(bx), taking LN of both sides gives LN(y) = LN(a) + bx — a linear equation you can fit with trendlines.
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