You should already be familiar with this expression \(\displaystyle{ 2^3 = 8 }\). This same expression written as a logarithm is \(\displaystyle{ 3 = \log_2 8 }\) and is read 'three is the logarithm (think:exponent) base two of eight' or 'three is log (think:power) eight base two'.
You could also say, if I have a base two and I want to get eight, what should the exponent (or power) of the base two be to get eight? The answer is three.

Let's pause for a minute and watch an interesting video talking about a unique way of looking at exponentials and logarithms.

It would be nice if all teachers used the triangle idea when thinking about exponentials and logarithms but things won't change overnight. So we need to study and be able to use the traditional way of looking at logarithms.

Before we go on, here is a great video for you that explains what logarithms are and how they work. It is well worth your time to watch it.

In calculus, you will work mostly with logarithms with base \(e\). These are special logarithms called natural logarithms. The notation is a bit different. Instead of \( \log_e x \), you will need to write \(\ln(x) \) or \( \ln ~x \). It is considered incorrect notation to write \( \log_e x \).