• The Excel LN function calculates the natural logarithm of a given number. The syntax of the function is: LN (number) where the number argument is the positive real number that you want to calculate the natural logarithm of.
• To calculate natural logarithm in Excel just use LN function. =LN(n) n = number. Base of natural logarithm is always e =LN(1) – result is 0 =LN(2.718281828) – result is 1 =LN(10) = result is 2.30258509 =LN(100) – result is 4.60517019 To calculate an inverse of natural logarithm use EXP function =EXP(n) n = number =EXP(0) – equals 1.
• The Excel LN function returns the natural logarithm of a given number.

You probably already know how to do standard graphs in Excel. Sometimes, you'll need to take it up another level and do logarithmical or semi-logarithmical graphs.Properly made graphs can give a concise and compact form of representation, while graphs made poorly can be misleading and very confusing.

Why use logarithmical graphs?

If you find yourself with data spread on an extremely large area, the graph will be very compact and you may miss some sharp drops in values because of this.

A semi-logarithmical graph is has one of the two axes (usually the abscissa) in a logarithmical form. The logarithmical base is usually 10, but can also be “e” or any other base.

How To Find Natural Log In Excel

That is why the logarithm that uses this number as its base is called a Natural logarithm. The value of e applies well to areas where the impact of the compound and continuous growth needs to be taken into consideration. As such, it has a lot of interesting applications, especially in the areas of finance and statistics.

Well let's suppose you have the following table:

X	1	2	5	10	20	50	100	200	500	1000	2000
Y	1	2	4	16	256	65536	4.29E+09	1.84E+19	3.4E+38	1.16E+77	1.3E+154

The corresponding Excel scatter chart is this:

On the other hand, if you extract the logarithm of both X and Y rows you get this table:

log_x	0	0.3	0.7	1	1.3	1.7	2	2.3	2.7	3	3.3
log_y	0	0.3	0.6	1.2	2.41	4.82	9.63	19.27	38.53	77.06	154.13

And its corresponding graph:

Does it make sense now? I thought so

How to obtain the logarithmic graph

Double click the axis that you want to be on a logarithmical scale. In the 'Scale' tab, select the 'Logarithmical Scale' option and click ok.

Then, go to the Chart Options (in the Chart menu) and in the 'Gridlines' tab check the 'Minor gridlines' on the axes you want depending of the desired graph type: semi-logarithmical or logarithmical.

Common (base ten) logarithms

The best way to understand logarithms is through an example. If you take 10 to the third power (10 x 10 x 10) the result is 1000. The logarithm is the inverse of that power function. The logarithm (base 10) of 1000 is the power of 10 that gives the answer 1000. So the logarithm of 1000 is 3. If you multiply 10 by itself 3 times, you get 1000.

You can take 10 to a negative power. For example, taking 10 to the -3 power is the same as taking the reciprocal of 10³. So 10^-3 equals 1/10³, or 0.001. The logarithm of 0.001 is the power of 10 that equals 0.001, which is -3.

You can take 10 to a fractional power. Ten to the 1/2 power equals the square root of 10, which is 3.163. So the logarithm of 3.163 is 0.5.

Ten to the zero power equals 1, so the logarithm of 1.0 is 0.0.

You can take the logarithm of any positive number. The logarithm of values between zero and one are negative; the logarithms of values greater than one are positive. The logarithms of zero and all negative numbers are undefined; there is no power of 10 that gives a negative number or zero.

Logarithms to other bases

The logarithms shown in the previous section are called base 10 logarithms, because the computations take 10 to some power. These are also called common logarithms.

Formula For Natural Log In Excel

You can compute logarithms for any power. Mathematicians prefer natural logarithms, using base e (2.7183…). Despite that name, use of logarithms with base e does not seem natural to most scientists who tend to be far more comfortable with base 10 logarithms.

Biologists sometimes use base 2 logarithms, often without realizing it. The base 2 logarithm is the number of doublings it takes to reach a value. So the log base 2 of 16 is 4 because if you start with 1 and double it four times (2, 4, 8, and 16) the result is 16. Immunologists often serially dilute antibodies by factors of 2, so often graph data on a log2 scale. Cell biologists use base 2 logarithms to convert cell counts to number of doublings.

Logarithms using different bases are proportional to each other. So converting from natural logs to common logs is sort of like changing units. Divide a natural logarithm by 2.303 to compute the common log of the same value. Multiply a common log by 2.303 to obtain the corresponding natural log.

Mathematical properties of logarithms

Logarithms convert multiplication into addition and division into subtraction, and exponentiation into mulitplication:

log(A^.B) = log(A) + log(B)

log(A/B) = log(A) - log(B)

log(Aⁿ) = n^.log(A)

Antilogarithms

The antilogarithm (also called an antilog) is the inverse of the logarithm transform. Since the logarithm (base 10) of 1000 equals 3, the antilogarithm of 3 is 1000. To compute the antilogarithm of a base 10 logarithm, take ten to that power.

To compute the antilogarithm of a natural logarithm, take e to that power. The natural logarithm of 1000 is 6.980. So the antilogarithm of 6.908 is e^6.908, which is 1000. Spreadsheets and computer languages use the notation exp(6.908).

Terms that sound similar to logarithm: logit and logistic

The term logistic sounds like it is related to logarithms. In fact, the term logistic has three distinct meanings, which don't all involve logarithms.

The logit function, used in logistic regression, is the natural logarithm of a probability (P, with a value between 0.0 and 1.0) divided by 1-P:

Logit(P) = ln[P/(1-P)]

The lognormal distribution is a distribution of values whose logarithms follow a Gaussian distribution. The lognormal distribution itself is asymmetrical with a heavy tail to the right. It is easy to be mislead by the asymmetry, and mistakenly eliminate values in the tail of the distribution as outliers.

The notation “log(x)” can be ambiguous

Within Prism transforms and equations, the log() function computes the common (base 10) logarithm.

With some computer languages (for example, Javascript) log(x) denotes a natural logarithm, not a common logarithm. Excel is especially confusing. In an Excel worksheet function, log(X) is the common logarithm, but in an Excel VBA macro, log(X) is the natural log.

The notation “ln(X)” is the natural logarithm in Prism.