Intro to Logarithms            Page 2 of 3

Changing Between Exponential and Logarithmic Form

You can rewrite an exponential equation as a logarithm and vice versa.  Remember, both forms always use the same base.  The base of the logarithm (the little number written after the word log) will be the same as the base of the exponent (the number that's being multiplied by itself).

Example 1
Rewrite in logarithmic form

First, identify the base.  2 is being raised to the 8th power - this means that 2 is the base.  The logarithm will have the same base, so we know to write a little 2 as a subscript after the word log.

Remember, a logarithm tells you what the exponent is.  In the exponential equation above, the exponent is 8.  This means the logarithm is equal to 8. The number after log base 2 is what you want the power to come out to - we want it to come out to 256.

​That's it! It's now in logarithmic form.

Example 2 
Rewrite in exponential form.

First, identify the base.  The exponential and logarithmic equations are both going to have the same base.  The equation is written in logarithmic form right now, so the base is the little number right after the word log - the 3.  This means our equation in exponential form will also have a base of 3.

The next step is to figure out what the exponent is.  Remember, the logarithm tells you what the exponent is.  This logarithm is equal to 6: this means the exponent is 6.  

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