Logarithms Complete Tutorial

Watch the videos and have fun learning about logarithms!

Expanding Logarithms

Using the properties of Logs

Condensing Logarithms

Using the properties of Logs

What is a logarithm?

A logarithmic function is the inverse of an exponential function. 

The graphs illustrate the key differences.

Exponential functionsThe y value increases more rapidly as the value of x increases.

Logarithmic functionsThe y value increases less rapidly as the value of x increase.

Logarithms – What do I need to learn?

  1. How to solve logarithms without a calculator.
  2. How to expand logarithms – Using the properties of logs
  3. How to condense logarithms – Using the properties of logs
  4. How to solve logarithmic equations.

Properties of Logarithms

Power property

The exponent or constant can be switched.


Quotient property



Two logs with a minus sign in the middle can be written as a single log with a quotient.



Product Property


Two logarithms with a plus sign can be written as a single log with a product.



Change of base property


Log properties



Natural log properties



Common application of logarithms

There are many applications of logarithms, but one of the most familiar is measuring earthquakes on the Richter scale. This is extremely useful, because the logarithmic scale allows use to measure earthquakes which can vary drastically in intensity. The logarithmic scale has a very small range (1-10) despite wide ranging intensity of all earthquakes. Each one point increase on the Richter scale means the earthquake is 10 times more powerful.  An earthquake measured at 6.0 on the Richter scale is considered strong. However, 6.0 quakes pale in comparison to a 7.0 quake (which is 10x stronger) or an 8.0 quake (which is 100x stronger).

Live Tutoring and Homework Solutions

I hope this page gave you a better understanding of logarithms. However, I understand some students still might need some extra help. This is because there is not enough time for me to make videos for every type of logarithm problem.

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