Question

How do you rewrite `log_5 125 = 3` in exponential form?

Answer 1

`log_5 125 = 3` can be rewritten as `5^3 = 125`.

Explanation:

When converting a logarithm to an exponential equation, the first thing you can do is disregard the word "log," since it won't be a logarithm anymore.

The base of our logarithm is `5`, and it will be the base of our exponential equation as well; `5` will be the number that will be raised to a power.

The product of our logarithm is `3`. In our exponential form, `3` will be the power. This is what we have so far:

`5^3` =

And you can see that the only thing left from our logarithm is `125`, and it will be converted to the exponential equation's product:

`5^3 = 125`

Check your work to make sure it's a true statement (it is), and you're good to go.

A common catchphrase for converting logarithms to exponential equations is "little to the right is the middle". Meaning you take the "little" number (the base) of the logarithm and raise it to the number on the far "right" (the product) of the logarithmic equation. And the "middle" number (the argument) of the logarithm is (equals) your product.

So in this case:
Little `= 5`
Right `= 3`
Middle `= 125`

`5^3 = 125`