How to calculate the logarithm of a number to a given base number using the LOG() function?

LOG(X, Y) is a MySQL built-in function that calculates the logarithm of Y to base X. For example:

SELECT LOG(2, 1024), LOG(2, 1.4142), LOG(2.718, 0.3679);
  -- +--------------+--------------------+---------------------+
  -- | LOG(2, 1024) | LOG(2, 1.4142)     | LOG(2.718, 0.3679)  |
  -- +--------------+--------------------+---------------------+
  -- |           10 | 0.4999861644218742 | -1.0000478060991969 |
  -- +--------------+--------------------+---------------------+

Reference information of the LOG() function:

LOG(Y, X): val
  Returns the logarithm of X to the base Y. If X is less than or equal to
  0, or if Y is less than or equal to 1, then NULL is returned.

  If called with one parameter Y, this function returns the natural
   logarithm of Y.

Arguments, return value and availability:
  Y: Required. The base value, if X is provided.
    It becomes a synonym for LN(Y), if X is not provided.
  X: Optional. The input value, if provided.
  val: Return value. The logarithm of the input value.
  Available since MySQL 4.0.

Related MySQL functions:

• POW() - X Raised to Power of Y

⇒ LOG10() - Logarithm to Base 10

⇐ LN() - Natural Logarithm

⇑ MySQL Functions on Numeric Values

⇑⇑ MySQL Function References