# Microsoft Knowledge Base

## Excel: Finding an Exponential Curve Using Natural Log

Last reviewed: September 12, 1996
Article ID: Q104449

• Microsoft Excel for Windows, versions 2.x, 3.0, 4.0, 4.0a
• Microsoft Excel for OS/2, version 2.2, 3.0
• Microsoft Excel for the Macintosh, version 2.x, 3.0, 4.0

## SUMMARY

In Microsoft Excel, the LOGEST() function calculates an exponential curve that fits data to the equation y=b*m^x and returns b and m for the given data.

If you want to use a natural logarithmic relation in the form of y=b*e^(n*x), then n should be taken to be equal to LN(m), where m is the value returned by LOGEST().

The LOGEST() function returns:

```   y=b*m^x
```

However, if you want LOGEST() return the natural log form, then the formula should be:

```   y=b*e^(n*x)
```

The above is algebraically derived as follows:

```   e^(n*x)=(e^n)^x
```

By substituting the above into e^(n*x)=(e^n)^x, it results in the following:

```   y=b*(e^n)^x.
```

LOGEST() returns b and m. By comparing the LOGEST() form y=b*m^x with the natural log form y=b*(e^n)^x, it is seen that e^n=m.

By taking the natural logarithm of each side of the equation, you get the following:

```   LN(e^n)=LN(m).
```

From the definitions for natural logarithms: LN(e)=1 and LN(e)^n=n*LN(m), you can conclude that LN(e)^n=n.

By substituting n=LN(m) into LN(e^n)=LN(m), you get LN(e^n)=n.

Earlier it was stated that LN(e^n)=LN(m). By substituting LN(e^n)=n into this formula, you get the following result: n=LN(m).

If you want to use the exponential curve in the form y=b*e^(n*x), you should use the LOGEST() function with your data. The results of the LOGEST() evaluates the m values returned with the natural logarithm function LN().

 KBCategory: kbusage KBSubcategory: Additional reference words: 2.00 3.00 4.00 4.00a THE INFORMATION PROVIDED IN THE MICROSOFT KNOWLEDGE BASE IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND. MICROSOFT DISCLAIMS ALL WARRANTIES, EITHER EXPRESS OR IMPLIED, INCLUDING THE WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL MICROSOFT CORPORATION OR ITS SUPPLIERS BE LIABLE FOR ANY DAMAGES WHATSOEVER INCLUDING DIRECT, INDIRECT, INCIDENTAL, CONSEQUENTIAL, LOSS OF BUSINESS PROFITS OR SPECIAL DAMAGES, EVEN IF MICROSOFT CORPORATION OR ITS SUPPLIERS HAVE BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. SOME STATES DO NOT ALLOW THE EXCLUSION OR LIMITATION OF LIABILITY FOR CONSEQUENTIAL OR INCIDENTAL DAMAGES SO THE FOREGOING LIMITATION MAY NOT APPLY. Last reviewed: September 12, 1996 ©1997 Microsoft Corporation. All rights reserved. Legal Notices.