LOG and EXP functions

The LOG(x) function returns the natural logarithm of the expression x. The returned result is of type FLOAT.

Starting with SQL Server 2012, this function received an optional argument for specifying the base of the logarithm.

SELECT LOG(2) ln, LOG(2, 10) log10;

This query returns the natural and the base-10 logarithms of 2.

Besides, there is the function LOG10(x) inherited from previous versions that returns the base-10 logarithm of the expression x. It has been redundant from the very beginning, since instead of it, the well-known change-of-base formula for logarithms can be used:

LOGba = LOGca/LOGcb

Thus, the following three expressions will return the same result (0.301029995663981):

SELECT LOG(2,10) log_1, LOG10(2) log_2, LOG(2)/LOG(10) log_3;

The function EXP(x), or the exponential function, returns the number e raised to the power of x. The returned result is of type FLOAT.

This function is inversely related to the LOG function:

SELECT EXP(LOG(2)) a, LOG(EXP(2)) b;

Another useful feature of logarithms - namely, the fact that the logarithm of a product is the sum of the logarithms of the factors - allows us to calculate the product of values in a column, i.e.

log(a*b*c) = log(a) + log(b) + log(c).

We can easily prove the correctness of this equality by the following example:

SELECT LOG(2*5*7) log_prod,  LOG(2) + LOG(5) + LOG(7) sum_log;

Among the SQL aggregate functions, there isn’t any for multiplying values. However, using the aforementioned feature of logarithms and some elementary transformations, we can reduce this task to calculating a sum of values. Indeed,

a*b*c = exp(log(a*b*c)) = exp(log(a) + log(b) + log(c)).

Solution

SELECT EXP(SUM(LOG(rn))) FROM(
SELECT ROW_NUMBER() OVER(ORDER BY code) rn FROM laptop
) X;

Suggested exercises: 106