Understanding Logarithms

Logarithm

In your junior class, you learned about indices where we write 2³ = 8. In this example, 2 is the base and 3 is the power or index.

Logarithm is just another way to talk about powers by looking at what power a base needs to reach a certain number.

We can write that the log of 8 to base 2 is equal to 3. We write it like this:

log₂ 8 = 3

Let us look at another example. We know that 5² = 25. This means that:

log₅ 25 = 2

A logarithm tells you the power you must give to a starting number to get a final number.

The log of any number N to base M is the index or power to which the base M must be raised to equal the number N.

This means the answer to a log question is simply the power that makes the base become the number you are looking at.

If x is the logarithm of a number N to base b, we write it as:

log_b N = x

Then, we can change it back to the index form like this:

N = b^x

To say it again clearly, if log_b N = x

Then,

N = b^x