What Is a Logarithm?

A logarithm is a type of function. There are multiple types of logarithms, but here we are looking at common logarithms.

Theory

The Common Logarithm

The common logarithm is also known as the decadic logarithm. It looks like this

\log (x), x > 0

It can also be written like this:

\log x \lg (x) \lg x

Theory

The Common Logarithm and the Number 10

These are some of the rules you use when solving logarithmic equations.

1 0^{\log x} = x \log 1 0^{x} = x

Logarithms can seem a bit odd, but they are just a special definition of a number: The logarithm to the number $x$ is the number $n$ that you have to use so that $1 0^{n} = x$

Like this:

\begin{array}{l} \log 1 & = 0 because 1 0^{0} = 1 \\ \log 100 & = 2 because 1 0^{2} = 100 \\ \log 0.001 & = - 3 because 1 0^{- 3} = 0.001 \end{array}

Example 1

Solve the logarithmic equation $\log x = 4$

\begin{array}{l} \log x & = 4 \\ 1 0^{\log x} & = 1 0^{4} \\ x & = 10 000 \end{array}

Example 2

Solve the equation $1 0^{x} = 3000$

\begin{array}{l} 1 0^{x} & = 3000 \\ \log 1 0^{x} & = \log 3000 \\ x & \approx 3.477 \end{array}

Want to know more?Sign UpIt's free!

What Is Euler's Number e?

Go back