Logarithms are simply another way to write exponents. Exponential and logarithmic functions are inverses of each other. For solving and graphing logarithmic functions (logs), remember this inverse relationship and you'll be solving logs in no time! Here's the relationship in equation form (the double arrow means "if and only if"):
Observe that x = by > 0.
Just as with exponential functions, the base can be any positive number except 1, including e. In fact, a base of e is so common in science and calculus that loge has its own special name: ln. Thus, logex = lnx.
Similarly, log10 is so commonly used that it's often just written as log (without the written base).