# Logarithm

## Logarithm

Logarithmic functions need to be graphed, which can look a little scary if you have never worked with them before. You will need your trusted pencil, a good eraser, and graphing paper to do this math problem. Even though it seems scary at first, it's not that bad once you get used to it. It's even less scary than when your sister tries to make dinner.

The opposite of an exponential function is a logarithmic function. The logarithmic function is y = a, while

The exponential function is written as x = ay. Remember that a must always be greater than 0 and can never be less than 0.

There are three main things about logarithms that make them useful:

logb(xy) = logbx + logby

logb(x/y) = logbx – logby.

logb(xn) = n logbx.

The fact that a logarithm is an exponent leads to these very simple properties of logarithms. The first property says that the log of a product is equal to the sum of the logs of its factors.

The second property says that the difference between the logs of the numerator and denominator is equal to the log of the quotient.

The third property says that the log of a power is equal to the power times the log of the base.

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Okay, by now you might be a little worried because these properties seem hard to take care of. To make things a little easier to understand, you should remember that a logarithm is just the power to which a number needs to be raised to get another number.

There are a lot of rules for logarithms, and they can be hard to understand if you don't know them in the right way. Here are some examples of some of the rules you will need to know:

The rule for the logarithm product is logb(x y) = logb(x) + logb (y)

Logarithm quotient rule is logb(x / y) = logb(x) – logb (y)

The rule for logarithm power is logb(x,y) = y logb (x)

The rule for switching the logarithm base is logb(c) = 1 / logc (b)

Before you can graph a logarithm, you need to turn it into an exponential expression. Remember that the exponential expression is the opposite of the log. Here's what you need to do:

1. Switch from a log to an exponential.
2. Figure out the opposite function. (To do this, you will switch x and y.)
3. Use the example below to draw a graph of the inverse function.

Now, that does not look too bad, does it! Logarithms take time to learn, so don't worry if you don't understand all the rules and properties right away. You will be able to master this function if you keep at it.

## Logarithms are a lot of fun:

John Napier's book, "Description of the Wonderful Rule of Logarithms," was the first to talk about logarithms in public. This new function went way beyond what algebraic methods are usually used for. This method became more popular than others, like the prosthaphaeresis, which had been used before.