## Excel LOGEST Function

The **LOGEST** function returns an exponential curve that best fits a supplied set of y- and x- values and returns an array of values that describes the curve.

#### Syntax

**=LOGEST(known_y’s,[known_x’s],[const],[stats])**

#### Arguments

**Known_y’s**(required): A set of known y-values.**Known_x’s**(optional): A set of known x-values. If provided, the data range of known_x's should have the same length as the data range of known_y’s. If omitted, it uses{1,2,3,...} as the known_y’s parameter.**Const**(optional): A logical value specifying whether the constant 'b', in the equation y=b * m^x, should be forced to be equal to the value 1. It is either a TRUE or FALSE value.

If const is TRUE or omitted, the constant b is calculated normally.

If const is FALSE, the constant b is set to 1 and the equation becomes y=m^x.**Stats**(optional): A logical value specifying whether additional regression statistics should be returned. It is either a TRUE or FALSE value.

If stats is FALSE or omitted, LOGEST returns only the m-coefficients and the constant b.

If stats is TRUE, LOGEST returns the additional regression statistics, so the returned array is {mn,mn-1,...,m1,b;sen,sen-1,...,se1,seb;r 2,sey; F,df;ssreg,ssresid}.

#### Return value

The **LOGEST** function returns a **numeric value**.

#### Function notes

- The LOGEST function returns an array of results and must be entered as an
**array formula**. Dynamic array formulas are available in**Excel 365**,**Excel 2021**, and**Excel for the web**, meaning no need to press**CTRL+SHIFT+ENTER**to make the formula**dynamic**. For users of**Excel 2019**and**earlier**, remember to enter the formula via**CTRL+SHIFT+ENTER**so the multiple results can be returned in an array. - The
**#REF!**error value occurs if the array of known_x’s is not the same length as the array of known_y’s. - The
**#VALUE!**error value occurs if any of the below situation occurs:- Any of the values in the supplied known_x’s or known_y’s arrays are
**non-numeric**; - Either the const or stats arguments cannot be evaluated to
**TRUE**or**FALSE**.

- Any of the values in the supplied known_x’s or known_y’s arrays are
- The equation for the curve is
**y=b*m^x**or**y=(b*(m1^x1)*(m2^x2)*_)**.

If there are multiple x-values, where the dependent y-value is a function of the independent x-values. The m-values are bases corresponding to each exponent x value, and b is a constant value. Note that y, x, and m can be vectors.

The array that LOGEST returns is {mn,mn-1,...,m1,b}. - The more a plot of your data resembles an exponential curve, the better the calculated line will fit your data. Both LINEST and LOGEST return an array of values that describes a relationship among the values, but LINEST fits a straight line to your data, whereas LOGEST fits an exponential curve.
- When you have only one independent x-variable, you can obtain y-intercept (b) values directly by using the following formula:
**Y-intercept (b): INDEX (LOGEST (known_y's,known_x's),2)**

You can use the**y=b*m^x**equation to predict future values of y, but the GROWTH Function does the same. - When entering an array constant such as known_x's as an argument, use commas to separate values in the same row and semicolons to separate rows. Separator characters may be different depending on your regional settings.
- You should note that the y-values predicted by the regression equation may not be valid if they are outside the range of y-values you used to determine the equation.

#### Example

As the below screenshot shows, there is a table of data with x and y values where x is the independent variable and y is the dependent variable. To use LOGEST to fit a curve to the data, please do as follows:

1. Select the cells to output the results, such as **H6** and **I6** in this case. Copy the formula below into the **Formula Bar**, then press the **CTRL+SHIFT+ENTER** keys to get the results.

**=LOGEST(C6:C10,B6:B10,E6,F6)**

**Note**: The result cell H6 contains the m value and result cell I6 contains the b value of the curve. The equation of the exponential curve for a single x variable is: y=b*m^x, where b=y-intercept of the curve, and m=the slope parameter of the curve.

#### Relative Functions:

Excel EVEN Function

The EVEN function rounds numbers away from zero to the nearest even integer.

Excel EXP Function

The EXP function returns the result of the constant e raised to the nth power.

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