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Why is a logarithm an exponennt and what is a logarithm exponent example?

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monique06 | Valedictorian

Posted May 31, 2013 at 2:33 PM via web

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Why is a logarithm an exponennt and what is a logarithm exponent example?

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 31, 2013 at 2:57 PM (Answer #1)

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A logarithm is an exponent because a logarithm is defined as:

`log_ax=b-gta^b=x`

Therefore, when you take the log of a function, the solution is an exponent.

For example:

`6^x=17` is difficult to solve because we know that the solution for x is not simply a whole number.  We can use what we know about logarithms to solve for it:

`log_6 17=x`

This is now solveable!  Not all calculators have the option of stating the base of the logarithm and offer only the two standards 10 and e (ln); therefore, you can solve this in a calculator by using the knowledge that:

`log_ax=logx/loga`

Where the log on the right side can be to any base (so you can use log or ln in your calculator).  Therefore:

`x=log_6 17=log17/log6=1.58`

Sources:

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