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

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### 1 Answer

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`

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